Question

graph the line with the equation $y = \frac{1}{6}x - 5$.

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 \(y=\frac{1}{6}x-5\), the slope \(m = \frac{1}{6}\) and the y - intercept \(b=- 5\). So, the line crosses the y - axis at the point \((0,-5)\).

Step2: Plot the y - intercept

Locate the point \((0, - 5)\) on the coordinate plane. This is the starting point for graphing the line.

Step3: Use the slope to find another point

The slope \(m=\frac{1}{6}\) can be thought of as \(\frac{\text{rise}}{\text{run}}\), which means for a run (change in \(x\)) of \(6\) units, the rise (change in \(y\)) is \(1\) unit. From the point \((0,-5)\), if we move \(6\) units to the right (increase \(x\) by \(6\)) to \(x = 6\), and then \(1\) unit up (increase \(y\) by \(1\)) from \(y=-5\) to \(y=-5 + 1=-4\), we get the point \((6,-4)\).

Step4: Draw the line

Draw a straight line through the points \((0,-5)\) and \((6,-4)\) (and extend it in both directions) to graph the line \(y=\frac{1}{6}x-5\).

Answer:

To graph \(y=\frac{1}{6}x - 5\), plot the y - intercept \((0,-5)\), then use the slope \(\frac{1}{6}\) to find another point (e.g., \((6,-4)\)) and draw a line through these points.