Question

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

Explanation:

Step1: Identify the slope and y - intercept

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

Step2: Plot the y - intercept

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

Step3: Use the slope to find another point

The slope \(m=\frac{1}{5}\) means that for every 5 units we move to the right (increase in \(x\) by 5), we move up 1 unit (increase in \(y\) by 1). Starting from the point \((0,-5)\), if we move 5 units to the right ( \(x = 0+5 = 5\)) and 1 unit up ( \(y=-5 + 1=-4\)), we get the point \((5,-4)\). We can also move in the opposite direction: for a slope of \(\frac{1}{5}\), the negative slope would be \(\frac{- 1}{-5}\), so if we move 5 units to the left ( \(x = 0 - 5=-5\)) and 1 unit down ( \(y=-5-1=-6\)), we get the point \((-5,-6)\).

Step4: Draw the line

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

(Note: Since the problem is about graphing, the final answer is the graph of the line with the equation \(y = \frac{1}{5}x-5\) passing through points like \((0, - 5)\), \((5,-4)\), \((-5,-6)\) etc. If we were to describe the key points: the y - intercept is at \((0,-5)\) and another point can be \((5,-4)\))

Answer:

The line \(y=\frac{1}{5}x - 5\) is graphed by plotting the y - intercept \((0,-5)\) and using the slope \(\frac{1}{5}\) to find additional points (e.g., \((5,-4)\)) and then drawing a straight line through them.