Question

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

Explanation:

Step1: Identify slope and y-intercept

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

Step2: Plot the y - intercept

The y - intercept is \( b=-1 \), so we plot the point \( (0,-1) \) 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 \( (0,-1) \), we rise 1 unit (upwards) and run 5 units (to the right). So we get the point \( (0 + 5,-1+1)=(5,0) \).

Step4: Draw the line

Draw a straight line passing through the points \( (0,-1) \) and \( (5,0) \). We can also find more points by using the slope in the opposite direction (rise - 1, run - 5) from \( (0,-1) \) to get \( (-5,-2) \) and draw the line through these points as well.

(Note: Since this is a graphing problem, the final answer is the graph of the line passing through points like \( (0,-1) \), \( (5,0) \), \( (-5,-2) \) etc. following the equation \( y=\frac{1}{5}x - 1 \))

Answer:

The line is graphed by plotting the y - intercept \( (0, - 1) \), using the slope \( \frac{1}{5} \) to find another point \( (5,0) \) (and others), and drawing a straight line through these points.