Question

graph the line.
$y = \frac{1}{4}x$

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=\frac{1}{4}x\), we can rewrite it as \(y=\frac{1}{4}x + 0\). So the slope \(m=\frac{1}{4}\) and the y - intercept \(b = 0\). This means the line passes through the origin \((0,0)\).

Step2: Use the slope to find another point

The slope \(m=\frac{\text{rise}}{\text{run}}=\frac{1}{4}\). Starting from the origin \((0,0)\), we move up 1 unit (rise) and then 4 units to the right (run). This gives us the point \((4,1)\) (since \(x = 0+4 = 4\) and \(y=0 + 1=1\)). We can also move down 1 unit and 4 units to the left from the origin to get the point \((- 4,-1)\) ( \(x=0 - 4=-4\) and \(y = 0-1=-1\)).

Step3: Plot the points and draw the line

Plot the points \((0,0)\), \((4,1)\) (and/or \((-4,-1)\)) on the coordinate plane. Then draw a straight line passing through these points.

Answer:

To graph \(y = \frac{1}{4}x\), plot the origin \((0,0)\) and the point \((4,1)\) (or \((-4,-1)\)) and draw a straight line through them. The line has a slope of \(\frac{1}{4}\) and passes through the origin.