Question 1

Find the constant of proportionality for the stated conditions: $E$ varies jointly with $I$ and $R$, and when $E$ $= 500 , R = 50$ and $\mathrm { I } = 2$.

Accepted Answer

A)  $\quad k = - 5$ 
B)  $\quad k = - 500$ 
C)  $\quad k = 500$ 
D)  $\quad k = 2$ 
E)  $\quad k = 5$ 
A)  $\quad k = - 5$ 
B)  $\quad k = - 500$ 
C)  $\quad k = 500$ 
D)  $\quad k = 2$ 
E)  $\quad k = 5$

Question 2

Find the equation of the line parallel to the line $x = 10$ and passing through the midpoint of the segment joining $( 9,7 )$ and $( 5 , - 3 )$.

Accepted Answer

A)  $\quad y = 2$ 
B)  $x = 7$ 
C)  $x = 9$ 
D)  $\quad x = 4$ 
E)  $\quad y = - 5$ 
A)  $\quad y = 2$ 
B)  $x = 7$ 
C)  $x = 9$ 
D)  $\quad x = 4$ 
E)  $\quad y = - 5$

Question 3

Determine whether the line through the points $P ( 40,18 ) , Q ( 26,20 )$ and the line through $R ( 20,9 )$, $S ( 13,10 )$ are parallel, perpendicular, or neither.

Accepted Answer

A)  neither 
B)  perpendicular 
C)  parallel 
A)  neither 
B)  perpendicular 
C)  parallel

Question 4

Decide which type of variation the graph represents.

Accepted Answer

A) direct variation 
B) neither 
C) inverse variation 
A) direct variation 
B) neither 
C) inverse variation

Question 5

$$\text { Find the midpoint of the line segment } P Q \text {. }$$ $P ( 4,7 ) , Q ( 2,5 )$

Accepted Answer

A)  $\quad M ( 1,0 )$ 
B)  $\quad M ( 3,6 )$ 
C)  $\quad M ( 5,6 )$ 
D)  $\quad M ( 8,9 )$ 
E)  $\quad M ( 3,5 )$ 
A)  $\quad M ( 1,0 )$ 
B)  $\quad M ( 3,6 )$ 
C)  $\quad M ( 5,6 )$ 
D)  $\quad M ( 8,9 )$ 
E)  $\quad M ( 3,5 )$

Question 6

Determine whether the line through the points $P ( 4,30 ) , Q ( 8,14 )$ and the line through $R ( 2,15 ) , S ( 4,7 )$ are parallel, perpendicular, or neither.

Accepted Answer

A)  neither 
B)  perpendicular 
C)  parallel 
A)  neither 
B)  perpendicular 
C)  parallel

Question 7

Find the slope of the line. $17 x - 5 = 15 ( y + x )$

Accepted Answer

A)  $\quad m = 17$ 
B)  $\quad m = 15$ 
C)  $\quad m = \frac { 17 } { 15 }$ 
D)  $m = - \frac { 2 } { 15 }$ 
E)  $m = \frac { 2 } { 15 }$
F) $m = \frac { 5 } { 17 }$ 
A)  $\quad m = 17$ 
B)  $\quad m = 15$ 
C)  $\quad m = \frac { 17 } { 15 }$ 
D)  $m = - \frac { 2 } { 15 }$ 
E)  $m = \frac { 2 } { 15 }$
F) $m = \frac { 5 } { 17 }$

Question 8

Determine whether the line through the points $P ( 8,34 ) , Q ( 12,16 )$ and the line through $R ( 4,17 ) , S ( 6,8 )$ are parallel, perpendicular, or neither.

Accepted Answer

A)  neither 
B)  parallel 
C)  perpendicular 
A)  neither 
B)  parallel 
C)  perpendicular

Question 9

For what value of $a$ does the equation $x ^ { 2 } + y ^ { 2 } - a x + 8 y + 16 = 0$ represent a circle with center $( 5 , - 4 ) ?$ When $a$ assumes this value, what is the radius of the circle?

Accepted Answer

A)  $\quad a = 9 , \quad$ radius $= 6$ 
B)  $\quad a = 10 , \quad$ radius $= 5$ 
C)  $\quad a = 8 , \quad$ radius $= 6$ 
D)  $\quad a = 9 , \quad$ radius $= 4$ 
E)  $\quad a = 11$, radius $= 7$ 
A)  $\quad a = 9 , \quad$ radius $= 6$ 
B)  $\quad a = 10 , \quad$ radius $= 5$ 
C)  $\quad a = 8 , \quad$ radius $= 6$ 
D)  $\quad a = 9 , \quad$ radius $= 4$ 
E)  $\quad a = 11$, radius $= 7$

Question 10

For what value of $a$ does the equation $x ^ { 2 } + y ^ { 2 } - a x + 4 y + - 3 = 0$ represent a circle with center $( 3 , - 2 )$ ? When $a$ assumes this value, what is the radius of the circle?

Accepted Answer

A)  $\quad a = 4 , \quad$ radius $= 5$ 
B)  $\quad a = 7 , \quad$ radius $= 6$ 
C)  $\quad a = 6 , \quad$ radius $= 4$ 
D)  $\quad a = 5 , \quad$ radius $= 5$ 
E)  $\quad a = 5 , \quad$ radius $= 3$ 
A)  $\quad a = 4 , \quad$ radius $= 5$ 
B)  $\quad a = 7 , \quad$ radius $= 6$ 
C)  $\quad a = 6 , \quad$ radius $= 4$ 
D)  $\quad a = 5 , \quad$ radius $= 5$ 
E)  $\quad a = 5 , \quad$ radius $= 3$

Question 11

Find the slope of the line. $11 x - 27 = 10 ( y + x )$

Accepted Answer

A)  $\quad m = \frac { 27 } { 11 }$ 
B)  $m = - \frac { 1 } { 10 }$ 
C)  $m = \frac { 11 } { 10 }$ 
D)  $m = 11$ 
E)  $m = \frac { 1 } { 10 }$
F) $m = 10$ 
A)  $\quad m = \frac { 27 } { 11 }$ 
B)  $m = - \frac { 1 } { 10 }$ 
C)  $m = \frac { 11 } { 10 }$ 
D)  $m = 11$ 
E)  $m = \frac { 1 } { 10 }$
F) $m = 10$

Question 12

For what value of $a$ does the equation $x ^ { 2 } + y ^ { 2 } - a x + 6 y + 33 = 0$ represent a circle with center $( 7 , - 3 )$ ? When $a$ assumes this value, what is the radius of the circle?

Accepted Answer

A)  $\quad a = 14$, radius $= 5$ 
B)  $\quad a = 13 , \quad$ radius $= 4$ 
C)  $\quad a = 13$, radius $= 6$ 
D)  $\quad a = 15 , \quad$ radius $= 7$ 
E)  $\quad a = 12 , \quad$ radius $= 6$ 
A)  $\quad a = 14$, radius $= 5$ 
B)  $\quad a = 13 , \quad$ radius $= 4$ 
C)  $\quad a = 13$, radius $= 6$ 
D)  $\quad a = 15 , \quad$ radius $= 7$ 
E)  $\quad a = 12 , \quad$ radius $= 6$

Question 13

Find the equation of the line parallel to the line $x = 2$ and passing through the midpoint of the segment joining $( 1,11 )$ and $( 7 , - 5 )$.

Accepted Answer

A)  $\quad y = - 7$ 
B)  $\quad x = - 6$ 
C)  $\quad x = 4$ 
D)  $\quad x = 1$ 
E)  $\quad y = 3$ 
A)  $\quad y = - 7$ 
B)  $\quad x = - 6$ 
C)  $\quad x = 4$ 
D)  $\quad x = 1$ 
E)  $\quad y = 3$

Question 14

The power, in watts, dissipated as heat in a resistor varies jointly with the resistance, in ohms, and the square of the current, in amperes.A 30-ohm resistor carrying a current of 1 ampere dissipates 30 watts.
How much power is dissipated in a 50-ohm resistor carrying a current of 8 amperes?

Accepted Answer

A)  $\quad P = 50$ Watts 
B)  $\quad P = 8$ Watts 
C)  $\quad P = 3,200$ Watts 
D)  $\quad P = 5$ Watts 
E)  $\quad P = 40$ Watts 
A)  $\quad P = 50$ Watts 
B)  $\quad P = 8$ Watts 
C)  $\quad P = 3,200$ Watts 
D)  $\quad P = 5$ Watts 
E)  $\quad P = 40$ Watts

Question 15

Find the slope of the line. $$y = 17 x + 29$$

Accepted Answer

A)  $\quad m = 17$ 
B)  $\quad m = 18$ 
C)  $\quad m = 14$ 
D)  $\quad m = 21$ 
E)  $\quad m = - 17$ 
A)  $\quad m = 17$ 
B)  $\quad m = 18$ 
C)  $\quad m = 14$ 
D)  $\quad m = 21$ 
E)  $\quad m = - 17$

Question 16

Find the slope of the line through $P ( - 8,8 )$ and $Q ( 1 , - 37 )$.

Accepted Answer

A)  $\quad m = - 4$ 
B)  $\quad m = - 7$ 
C)  $\quad m = - 3$ 
D)  $m = - 5$ 
E)  $\quad m = - 6$ 
A)  $\quad m = - 4$ 
B)  $\quad m = - 7$ 
C)  $\quad m = - 3$ 
D)  $m = - 5$ 
E)  $\quad m = - 6$

Question 17

Use the slope-intercept form to write the equation of the line passing through the point $P ( 16,0 )$ and having the slope $m = - \frac { 1 } { 4 }$. Express the answer in general form.

Accepted Answer

A)  $\quad x - 4 y = - 12$ 
B)  $\quad x + 4 y = 16$ 
C)  $\quad x + 4 y = - 16$ 
D)  $\quad y = \frac { 1 } { 4 } x + 1$ 
E)  $x - 4 y = 16$ 
A)  $\quad x - 4 y = - 12$ 
B)  $\quad x + 4 y = 16$ 
C)  $\quad x + 4 y = - 16$ 
D)  $\quad y = \frac { 1 } { 4 } x + 1$ 
E)  $x - 4 y = 16$

Question 18

Find the x-intercept of the function. $$9 x + 8 y = 16$$

Accepted Answer

A)  $( 9 / 16,0 )$ 
B)  $\quad ( 0,2 )$ 
C)  $( 2,0 )$ 
D)  $\quad ( 0,16 / 9 )$ 
E)  $( 16 / 9,0 )$ 
A)  $( 9 / 16,0 )$ 
B)  $\quad ( 0,2 )$ 
C)  $( 2,0 )$ 
D)  $\quad ( 0,16 / 9 )$ 
E)  $( 16 / 9,0 )$

Question 19

Graph the equation. $$y = x ^ { 2 } + 5 x$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 20

Indicate the quadrant in which the point $( - 6 , - 1 )$ lies.

Accepted Answer

A)  quadrant III 
B)  quadrant II 
C)  quadrant I 
D)  quadrant IV 
E)  none of these 
A)  quadrant III 
B)  quadrant II 
C)  quadrant I 
D)  quadrant IV 
E)  none of these

Find the constant of proportionality for the stated conditions: $E$ varies jointly with $I$ and $R$ , and when $E$ $= 500 , R = 50$ and $\mathrm { I } = 2$ .

Find the equation of the line parallel to the line $x = 10$ and passing through the midpoint of the segment joining $( 9,7 )$ and $( 5 , - 3 )$ .

Determine whether the line through the points $P ( 40,18 ) , Q ( 26,20 )$ and the line through $R ( 20,9 )$ , $S ( 13,10 )$ are parallel, perpendicular, or neither.

Decide which type of variation the graph represents.

$\text { Find the midpoint of the line segment } P Q \text {. }$ $P ( 4,7 ) , Q ( 2,5 )$

Determine whether the line through the points $P ( 4,30 ) , Q ( 8,14 )$ and the line through $R ( 2,15 ) , S ( 4,7 )$ are parallel, perpendicular, or neither.

Find the slope of the line. $17 x - 5 = 15 ( y + x )$

Determine whether the line through the points $P ( 8,34 ) , Q ( 12,16 )$ and the line through $R ( 4,17 ) , S ( 6,8 )$ are parallel, perpendicular, or neither.

For what value of $a$ does the equation $x ^ { 2 } + y ^ { 2 } - a x + 8 y + 16 = 0$ represent a circle with center $( 5 , - 4 ) ?$ When $a$ assumes this value, what is the radius of the circle?

For what value of $a$ does the equation $x ^ { 2 } + y ^ { 2 } - a x + 4 y + - 3 = 0$ represent a circle with center $( 3 , - 2 )$ ? When $a$ assumes this value, what is the radius of the circle?

Find the slope of the line. $11 x - 27 = 10 ( y + x )$

For what value of $a$ does the equation $x ^ { 2 } + y ^ { 2 } - a x + 6 y + 33 = 0$ represent a circle with center $( 7 , - 3 )$ ? When $a$ assumes this value, what is the radius of the circle?

Find the equation of the line parallel to the line $x = 2$ and passing through the midpoint of the segment joining $( 1,11 )$ and $( 7 , - 5 )$ .

The power, in watts, dissipated as heat in a resistor varies jointly with the resistance, in ohms, and the square of the current, in amperes.A 30-ohm resistor carrying a current of 1 ampere dissipates 30 watts. How much power is dissipated in a 50-ohm resistor carrying a current of 8 amperes?

Find the slope of the line. $y = 17 x + 29$

Find the slope of the line through $P ( - 8,8 )$ and $Q ( 1 , - 37 )$ .

Use the slope-intercept form to write the equation of the line passing through the point $P ( 16,0 )$ and having the slope $m = - \frac { 1 } { 4 }$ . Express the answer in general form.

Find the x-intercept of the function. $9 x + 8 y = 16$

Graph the equation. $y = x ^ { 2 } + 5 x$

Indicate the quadrant in which the point $( - 6 , - 1 )$ lies.

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Exam 3: The Rectangular Coordinate System and Graphs of Equations

Find the constant of proportionality for the stated conditions: EEE varies jointly with III and RRR , and when EEE =500,R=50= 500 , R = 50=500,R=50 and I=2\mathrm { I } = 2I=2 .

Find the equation of the line parallel to the line x=10x = 10x=10 and passing through the midpoint of the segment joining (9,7)( 9,7 )(9,7) and (5,−3)( 5 , - 3 )(5,−3) .

Determine whether the line through the points P(40,18),Q(26,20)P ( 40,18 ) , Q ( 26,20 )P(40,18),Q(26,20) and the line through R(20,9)R ( 20,9 )R(20,9) , S(13,10)S ( 13,10 )S(13,10) are parallel, perpendicular, or neither.

Decide which type of variation the graph represents.

Find the midpoint of the line segment PQ. \text { Find the midpoint of the line segment } P Q \text {. } Find the midpoint of the line segment PQ. P(4,7),Q(2,5)P ( 4,7 ) , Q ( 2,5 )P(4,7),Q(2,5)

Determine whether the line through the points P(4,30),Q(8,14)P ( 4,30 ) , Q ( 8,14 )P(4,30),Q(8,14) and the line through R(2,15),S(4,7)R ( 2,15 ) , S ( 4,7 )R(2,15),S(4,7) are parallel, perpendicular, or neither.

Find the slope of the line. 17x−5=15(y+x)17 x - 5 = 15 ( y + x )17x−5=15(y+x)

Determine whether the line through the points P(8,34),Q(12,16)P ( 8,34 ) , Q ( 12,16 )P(8,34),Q(12,16) and the line through R(4,17),S(6,8)R ( 4,17 ) , S ( 6,8 )R(4,17),S(6,8) are parallel, perpendicular, or neither.

For what value of aaa does the equation x2+y2−ax+8y+16=0x ^ { 2 } + y ^ { 2 } - a x + 8 y + 16 = 0x2+y2−ax+8y+16=0 represent a circle with center (5,−4)?( 5 , - 4 ) ?(5,−4)? When aaa assumes this value, what is the radius of the circle?

For what value of aaa does the equation x2+y2−ax+4y+−3=0x ^ { 2 } + y ^ { 2 } - a x + 4 y + - 3 = 0x2+y2−ax+4y+−3=0 represent a circle with center (3,−2)( 3 , - 2 )(3,−2) ? When aaa assumes this value, what is the radius of the circle?

Find the slope of the line. 11x−27=10(y+x)11 x - 27 = 10 ( y + x )11x−27=10(y+x)

For what value of aaa does the equation x2+y2−ax+6y+33=0x ^ { 2 } + y ^ { 2 } - a x + 6 y + 33 = 0x2+y2−ax+6y+33=0 represent a circle with center (7,−3)( 7 , - 3 )(7,−3) ? When aaa assumes this value, what is the radius of the circle?

Find the equation of the line parallel to the line x=2x = 2x=2 and passing through the midpoint of the segment joining (1,11)( 1,11 )(1,11) and (7,−5)( 7 , - 5 )(7,−5) .

The power, in watts, dissipated as heat in a resistor varies jointly with the resistance, in ohms, and the square of the current, in amperes.A 30-ohm resistor carrying a current of 1 ampere dissipates 30 watts. How much power is dissipated in a 50-ohm resistor carrying a current of 8 amperes?

Find the slope of the line. y=17x+29y = 17 x + 29y=17x+29

Find the slope of the line through P(−8,8)P ( - 8,8 )P(−8,8) and Q(1,−37)Q ( 1 , - 37 )Q(1,−37) .

Use the slope-intercept form to write the equation of the line passing through the point P(16,0)P ( 16,0 )P(16,0) and having the slope m=−14m = - \frac { 1 } { 4 }m=−41​ . Express the answer in general form.

Find the x-intercept of the function. 9x+8y=169 x + 8 y = 169x+8y=16

Graph the equation. y=x2+5xy = x ^ { 2 } + 5 xy=x2+5x

Indicate the quadrant in which the point (−6,−1)( - 6 , - 1 )(−6,−1) lies.

A Review of Basic Algebra

Equations and Inequalities

Functions Functions and Function Notation

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Solving Polynomial Equations

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Find the constant of proportionality for the stated conditions: $E$ varies jointly with $I$ and $R$ , and when $E$ $= 500 , R = 50$ and $\mathrm { I } = 2$ .

Find the equation of the line parallel to the line $x = 10$ and passing through the midpoint of the segment joining $( 9,7 )$ and $( 5 , - 3 )$ .

Determine whether the line through the points $P ( 40,18 ) , Q ( 26,20 )$ and the line through $R ( 20,9 )$ , $S ( 13,10 )$ are parallel, perpendicular, or neither.

$\text { Find the midpoint of the line segment } P Q \text {. }$ $P ( 4,7 ) , Q ( 2,5 )$

Determine whether the line through the points $P ( 4,30 ) , Q ( 8,14 )$ and the line through $R ( 2,15 ) , S ( 4,7 )$ are parallel, perpendicular, or neither.

Find the slope of the line. $17 x - 5 = 15 ( y + x )$

Determine whether the line through the points $P ( 8,34 ) , Q ( 12,16 )$ and the line through $R ( 4,17 ) , S ( 6,8 )$ are parallel, perpendicular, or neither.

For what value of $a$ does the equation $x ^ { 2 } + y ^ { 2 } - a x + 8 y + 16 = 0$ represent a circle with center $( 5 , - 4 ) ?$ When $a$ assumes this value, what is the radius of the circle?

For what value of $a$ does the equation $x ^ { 2 } + y ^ { 2 } - a x + 4 y + - 3 = 0$ represent a circle with center $( 3 , - 2 )$ ? When $a$ assumes this value, what is the radius of the circle?

Find the slope of the line. $11 x - 27 = 10 ( y + x )$

For what value of $a$ does the equation $x ^ { 2 } + y ^ { 2 } - a x + 6 y + 33 = 0$ represent a circle with center $( 7 , - 3 )$ ? When $a$ assumes this value, what is the radius of the circle?

Find the equation of the line parallel to the line $x = 2$ and passing through the midpoint of the segment joining $( 1,11 )$ and $( 7 , - 5 )$ .

Find the slope of the line. $y = 17 x + 29$

Find the slope of the line through $P ( - 8,8 )$ and $Q ( 1 , - 37 )$ .

Use the slope-intercept form to write the equation of the line passing through the point $P ( 16,0 )$ and having the slope $m = - \frac { 1 } { 4 }$ . Express the answer in general form.

Find the x-intercept of the function. $9 x + 8 y = 16$

Graph the equation. $y = x ^ { 2 } + 5 x$

Indicate the quadrant in which the point $( - 6 , - 1 )$ lies.