Exam 2: Linear Models, Equations, and Inequalities

You are given a table showing input and output values for a given function $y _ { 1 } = f ( x )$ x). Use the table to answer the question. -What is the $y$ -intercept of the graph of $y = f ( x )$ ?

You are given a table showing input and output values for a given function $y _ { 1 } = f ( x )$ x). Use the table to answer the question. -What is the $x$ -intercept of the graph of $y = f ( x )$ ?

Solve the equation. - $( y - 7 ) - ( y + 2 ) = 4 y$

Solve the equation. - $6 ( 3 x - 1 ) = 24$

Solve the inequality and draw a number line graph of the solution. - $0.5 a > 7$

Solve the equation. - $9 x - ( 4 x - 1 ) = 2$

Provide an appropriate response. - $\text { If } a \leq b \text {, is it always true that } a + 6 \leq b + 6$ ? Explain.

Solve the double inequality. - $- 8 \leq 0.2 z + 3 \leq - 5$

To find the number of units that gives break-even for the product, solve the equation R $\mathbf { R } = \mathbf { C }$ ound your answer to the nearest whole unit. -Suppose that the number of inhabitants of Country A is given by $y = - 7.33 x + 909.51$ million, and the number of inhabitants of Country B is given by $y = 2.07 x + 815.51$ million, where $x$ is the number of years since 2010 . Find the year in which the number of inhabitants of Country A equals the number of inhabitants of Country B.

Solve the double inequality. - $- 5 < \frac { 6 - 5 x } { 10 } \leq 3$

Translate the sentence to an algebraic inequality. -The cost is no more than $336.95.

Find the linear function that is the best fit for the given data. Round decimal values to the nearest hundredth, if necessary. - 1.2 1.4 1.6 1.8 2.0 54 53 55 54 56

Does the system have a unique solution, no solution, or many solutions? - $\left\{ \begin{array} { l } x + y = 7 \\x + y = 8\end{array} \right.$

Provide an appropriate response. - $\text { If } a < b \text {, is it always true that } \frac { 1 } { a } > \frac { 1 } { b } \text { ? Explain. }$

Provide an appropriate response. - $\text { If } a \leq b \text {, is it always true that } - 4 a \leq - 4 b$ ? Explain.

Solve the system of equations by elimination, if a solution exists. - $\left\{ \begin{array} { c } 8 x + 9 y = 8 \\- 5 x + 7 y = - 5\end{array} \right.$

Solve the double inequality. - $- 13 < - 3 a + 5$ and $- 3 a + 5 \leq - 1$

Translate the sentence to an algebraic inequality. -A salesperson has two job offers. Company A offers a weekly salary of $400 plus commission of 10% of sales. Company B offers a weekly salary of $800 plus commission of 5% of sales. What is the amount of sales above Which Company A's offer is the better of the two?

Solve the equation for y. -An average score of 90 for 5 exams is needed for a final grade of A. John's first 4 exam grades are 79, 89, 97, and 95. Determine the grade needed on the fifth exam to get an A in the course.

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ . -