Question

select any two points shown on line g to draw a slope triangle. the line decreases from left to right. therefore, the slope is negative. enter the slope of line g: - 1/3. enter a number to complete the equation for line g: y = - 1/3x. press the button to translate line g down 5 units. enter numbers to complete the equation for line g: y = - 1/3x+( )

Explanation:

Step1: Recall translation rule

For a linear - function \(y = mx + b\), translating the line down \(k\) units gives the new function \(y=mx+(b - k)\). The original equation of line \(g\) is \(y =-\frac{1}{3}x\), which is in the form \(y = mx + b\) where \(m =-\frac{1}{3}\) and \(b = 0\).

Step2: Apply the translation

We want to translate the line down 5 units. Using the rule \(y=mx+(b - k)\), with \(m =-\frac{1}{3}\), \(b = 0\), and \(k = 5\), the new equation is \(y=-\frac{1}{3}x+(0 - 5)\).

Step3: Simplify the equation

\(y=-\frac{1}{3}x-5\)

Answer:

\(y =-\frac{1}{3}x-5\)