Question

y = -\frac{1}{6}x - 7
click to select points on the graph.
(graph with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines, and two equations at the bottom: y = -\frac{1}{6}x + 6 (purple) and y = -\frac{1}{6}x - 7 (green))

Explanation:

Step1: Find the y - intercept

The equation of the line is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the line \(y=-\frac{1}{6}x - 7\), when \(x = 0\), we substitute \(x = 0\) into the equation:
\(y=-\frac{1}{6}(0)-7=-7\). So the y - intercept is the point \((0,-7)\).

Step2: Find another point using the slope

The slope \(m =-\frac{1}{6}\), which means for a run of \(6\) (change in \(x\)) of \(6\) units (we can choose a positive or negative run, let's choose a run of \(6\) to the right, so \(\Delta x=6\)), the change in \(y\) (\(\Delta y\)) is \(- 1\) (since \(m=\frac{\Delta y}{\Delta x}\)).
Starting from the y - intercept \((0,-7)\), if we move \(x = 0+6 = 6\), then \(y=-7+(-1)=-8\). So another point on the line is \((6,-8)\). We can also check with a run of \(- 6\) (moving \(6\) units to the left). If \(x=0 - 6=-6\), then \(y=-\frac{1}{6}(-6)-7 = 1-7=-6\), so the point \((-6,-6)\) is also on the line.

To graph the line \(y =-\frac{1}{6}x-7\), we plot the points \((0,-7)\) and \((6,-8)\) (or \((-6,-6)\)) and draw a straight line through them.

Answer:

To graph \(y =-\frac{1}{6}x - 7\), plot the y - intercept \((0,-7)\) and use the slope \(-\frac{1}{6}\) to find another point (e.g., \((6,-8)\) or \((-6,-6)\)) and draw a line through these points. The key points are \((0,-7)\) and, for example, \((6,-8)\).