Question

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

Explanation:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=-\frac{1}{5}x + 6\), the y - intercept \(b = 6\). So we plot the point \((0,6)\) on the graph.

Step2: Use the slope to find another point

The slope \(m=-\frac{1}{5}\), which means for a run (change in \(x\)) of \(5\) units, the rise (change in \(y\)) is \(- 1\) unit (or for a run of \(- 5\) units, the rise is \(1\) unit). Starting from the y - intercept \((0,6)\), if we move \(5\) units to the right (increase \(x\) by \(5\)) to \(x = 5\), then we move down \(1\) unit (decrease \(y\) by \(1\)) to \(y=6 - 1=5\). So we can plot the point \((5,5)\). Alternatively, if we move \(5\) units to the left (decrease \(x\) by \(5\)) to \(x=-5\), we move up \(1\) unit (increase \(y\) by \(1\)) to \(y = 6+1 = 7\), and plot the point \((-5,7)\).

Step3: Draw the line

After plotting at least two points (e.g., \((0,6)\) and \((5,5)\) or \((0,6)\) and \((-5,7)\)), we draw a straight line passing through these points.

Answer:

To graph the line \(y =-\frac{1}{5}x + 6\), plot the y - intercept \((0,6)\) and another point (e.g., \((5,5)\) or \((-5,7)\)) using the slope, then draw a straight line through the plotted points.