Question

graph these equations:
$y = -\frac{1}{5}x$
$y = -\frac{1}{5}x - 4$
click to select points on the graph.

Explanation:

Step1: Analyze \( y = -\frac{1}{5}x \)

This is a linear equation in slope - intercept form \( y=mx + b \) where \( m = -\frac{1}{5} \) and \( b = 0 \). So it passes through the origin \((0,0)\). To find another point, let's take \( x = 5 \), then \( y=-\frac{1}{5}\times5=- 1 \), so the point \((5, - 1)\) is on this line.

Step2: Analyze \( y=-\frac{1}{5}x - 4 \)

This is also a linear equation in slope - intercept form with \( m=-\frac{1}{5} \) and \( b=-4 \). The y - intercept is at \((0,-4)\). To find another point, let \( x = 5 \), then \( y=-\frac{1}{5}\times5-4=-1 - 4=-5 \), so the point \((5,-5)\) is on this line.

Step3: Graphing the lines

• For \( y = -\frac{1}{5}x \), plot the points \((0,0)\) and \((5, - 1)\) (and other points if needed) and draw a straight line through them.
• For \( y=-\frac{1}{5}x - 4 \), plot the points \((0,-4)\) and \((5,-5)\) (and other points if needed) and draw a straight line through them. The two lines should be parallel since they have the same slope (\(m = -\frac{1}{5}\)) and different y - intercepts.

Answer:

To graph \( y = -\frac{1}{5}x \): Plot \((0,0)\) and \((5, - 1)\) (or other points) and draw a line. To graph \( y=-\frac{1}{5}x - 4 \): Plot \((0,-4)\) and \((5,-5)\) (or other points) and draw a line. The two lines are parallel.