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 \(m=-\frac{1}{5}=\frac{\text{rise}}{\text{run}}\), which means for every 5 units we move to the right (run = 5), we move down 1 unit (rise=- 1), or for every 5 units we move to the left (run=-5), we move up 1 unit (rise = 1).

Step2: Find another point using the slope

Starting from the y - intercept \((0,6)\), using the slope \(m =-\frac{1}{5}\), if we move \(x = 5\) units to the right (so \(x=0 + 5=5\)), then \(y=6-\frac{1}{5}(5)=6 - 1 = 5\). So the point \((5,5)\) is on the line. Or if we move \(x=- 5\) units (to the left), \(y=6-\frac{1}{5}(-5)=6 + 1=7\), so the point \((-5,7)\) is on the line. We can use one of these points (or any other point found using the slope) and draw a straight line through the y - intercept \((0,6)\) and this new point.

Answer:

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

1. Plot the y - intercept \((0,6)\) (already plotted in the given graph).
2. Use the slope \(m =-\frac{1}{5}\) to find another point. For example, from \((0,6)\), move 5 units to the right (along the x - axis) and 1 unit down (along the y - axis) to get the point \((5,5)\), or 5 units to the left and 1 unit up to get \((-5,7)\).
3. Draw a straight line through the plotted y - intercept and the new point.