Question

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

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 \(y=\frac{1}{5}x + 2\), the slope \(m=\frac{1}{5}\) and the y - intercept \(b = 2\).

Step2: Plot the y - intercept

The y - intercept is \(b = 2\), which means the line crosses the y - axis at the point \((0,2)\). Locate the point \((0,2)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m=\frac{1}{5}\) can be thought of as \(\frac{\text{rise}}{\text{run}}=\frac{1}{5}\). From the point \((0,2)\), we can move up 1 unit (rise) and then move 5 units to the right (run) to get the next point. So, starting from \((0,2)\), moving up 1 and right 5 gives us the point \((0 + 5,2+1)=(5,3)\). We can also move down 1 unit and left 5 units from \((0,2)\) to get another point \((0 - 5,2-1)=(-5,1)\).

Step4: Draw the line

Using a straightedge, draw a line that passes through the points we found (such as \((0,2)\), \((5,3)\) and \((-5,1)\)). Extend the line in both directions to show the entire line.

Answer:

To graph \(y=\frac{1}{5}x + 2\), plot \((0,2)\), then use the slope \(\frac{1}{5}\) to find other points (e.g., \((5,3)\) or \((-5,1)\)) and draw a straight line through them.