91Ó°ÊÓ

\(y\) varies directly with \(x\). If \(y=30\) when \(x=-3,\) find \(y\) when \(x=-9\)

Writing When you graph an inequality, you can often use the point \((0,0)\) to test which side of the boundary line to shade. Describe a situation in which you could not use \((0,0)\) as a test point.

Find the range of each function when the domain is \(\\{-3,-1,0,1.5,4\\}\). $$ y=9-2 x $$

Graph each absolute value equation. $$ y=-|-2 x-1|+1 $$

Graph each inequality on a graphing calculator. Then sketch the graph. $$ y<|x-3|-|x+3| $$

Graph each absolute value equation. $$ -3 y=|3 x-6| $$

Suppose you drive a car 392 mi on one tank of gas. The tank holds 14 gallons. The number of miles traveled varies directly with the number of gallons of gas you use. a. Write an equation that relates miles traveled to gallons of gas used. b. You only have enough money to buy 3.7 gallons of gas. How far can you drive before refueling? c. Last year you drove \(11,700\) mi. About how many gallons of gas did you use? d. Suppose the price of gas averaged \(\$ 1.57\) per gallon last year. Find the cost per mile.

Suppose you use the origin to test whether a linear equation is a direct variation. Does this method work? Support your answer with an example.

Graph each function by translating its parent function. $$ y=|x|-3 $$

Find the slope and the intercepts of each line. $$ y=-x+1000 $$