Question

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

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 \(y=-\frac{1}{5}x + 6\), the y - intercept \(b = 6\), so the line crosses the y - axis at \((0,6)\) (this point is already plotted). The slope \(m=-\frac{1}{5}\), which means for every 5 units we move to the right (increase in \(x\) by 5), we move down 1 unit (decrease in \(y\) by 1), or for every 5 units we move to the left (decrease in \(x\) by 5), we move up 1 unit (increase in \(y\) by 1).

Step2: Find another point using the slope

Starting from the y - intercept \((0,6)\), using the slope \(m =-\frac{1}{5}\), if we let \(x = 5\), then \(y=-\frac{1}{5}(5)+6=- 1 + 6 = 5\). So the point \((5,5)\) is on the line. If we let \(x=- 5\), then \(y =-\frac{1}{5}(-5)+6 = 1+6=7\), so the point \((-5,7)\) is also on the line. We can use one of these points (e.g., \((5,5)\)) and draw a straight line through \((0,6)\) and \((5,5)\) (or other points found using the slope) to graph the line.

Answer:

To graph \(y =-\frac{1}{5}x + 6\):

1. Plot the y - intercept \((0,6)\) (already plotted in the given graph).
2. Use the slope \(m =-\frac{1}{5}\): From \((0,6)\), move 5 units right (to \(x = 5\)) and 1 unit down (to \(y=5\)) to get the point \((5,5)\), or move 5 units left (to \(x=-5\)) and 1 unit up (to \(y = 7\)) to get the point \((-5,7)\).
3. Draw a straight line through the plotted points (e.g., \((0,6)\) and \((5,5)\) or \((0,6)\) and \((-5,7)\)) to represent the line \(y=-\frac{1}{5}x + 6\).