Question

graph the line with the equation $y = \frac{1}{5}x - 5$.

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = \frac{1}{5}x - 5 \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{1}{5} \) (slope) and \( b = - 5 \) (y - intercept).

Step2: Plot the y - intercept

The y - intercept is \( b=-5 \), so we plot the point \( (0,-5) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m = \frac{1}{5}=\frac{\text{rise}}{\text{run}} \). From the point \( (0,-5) \), we rise 1 unit (move up 1) and run 5 units (move to the right 5). This gives us the point \( (0 + 5,-5+1)=(5,-4) \). We can also go in the opposite direction: from \( (0,-5) \), rise - 1 (move down 1) and run - 5 (move to the left 5) to get the point \( (0-5,-5 - 1)=(-5,-6) \).

Step4: Draw the line

Draw a straight line through the plotted points \( (0,-5) \), \( (5,-4) \) (or other points found using the slope) to graph the line \( y=\frac{1}{5}x - 5 \).

Answer:

To graph \( y=\frac{1}{5}x - 5 \):

1. Plot the y - intercept at \( (0,-5) \).
2. Use the slope \( \frac{1}{5} \) to find another point (e.g., \( (5,-4) \)) and plot it.
3. Draw a straight line through these points. The line should pass through \( (0,-5) \), \( (5,-4) \), \( (-5,-6) \) etc. (The actual graph is a straight line with the described characteristics on the given coordinate grid.)