Question

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

Explanation:

Step1: Recall translation rule

When a line \(y = mx + b\) is translated down \(k\) units, the new - equation is \(y=mx+(b - k)\). The slope \(m\) remains the same during a vertical translation.
The original line \(r\) has the equation \(y =-\frac{1}{5}x\), which is in the form \(y = mx + b\) where \(m =-\frac{1}{5}\) and \(b = 0\).

Step2: Apply the translation

We are translating the line down 5 units (\(k = 5\)). Since the slope \(m\) of the original line \(r\) is \(-\frac{1}{5}\), the slope of the new line \(s\) is also \(-\frac{1}{5}\).
The \(y\) - intercept \(b\) of the original line \(r\) is 0. After translating the line down 5 units, the new \(y\) - intercept \(b_{new}=0 - 5=-5\).
The equation of line \(s\) is \(y =-\frac{1}{5}x-5\).

Answer:

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