Question

graph the line.
$y = \frac{1}{5}x - 2$

Explanation:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=\frac{1}{5}x - 2\), \(b=- 2\). So the line crosses the y - axis at \((0,-2)\).

Step2: Use the slope to find another point

The slope \(m=\frac{1}{5}\), which means 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 \((0,-2)\), if we move \(x = 5\) (so \(x=0 + 5=5\)), then \(y=-2+\frac{1}{5}\times5=-2 + 1=-1\). So another point on the line is \((5,-1)\). We can also find a point by moving left: if \(x=- 5\), then \(y=\frac{1}{5}\times(-5)-2=-1 - 2=-3\), so the point is \((-5,-3)\).

Step3: Plot the points and draw the line

Plot the points \((0,-2)\), \((5,-1)\) (or \((-5,-3)\)) on the coordinate plane and then draw a straight line through them.

(Note: Since the actual graph drawing is a visual task, the key is to identify the correct points based on the slope - intercept form. The y - intercept is \((0,-2)\) and using the slope \(\frac{1}{5}\) to find additional points helps in graphing the line accurately.)

Answer:

To graph \(y = \frac{1}{5}x-2\), plot the y - intercept \((0, - 2)\) and use the slope \(\frac{1}{5}\) (rise 1, run 5) to find another point (e.g., \((5,-1)\) or \((-5,-3)\)) and draw a line through these points.