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 axes arrows)

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

Let's choose a value of \(x\) that makes the calculation easy. Let's take \(x = 6\) (because the denominator of the slope is 6, this will make the \(x\) term an integer).
Substitute \(x = 6\) into the equation \(y =-\frac{1}{6}x-7\):
\(y=-\frac{1}{6}(6)-7=- 1-7=-8\)
So the point \((6, - 8)\) is also on the line.

To graph the line, we can plot the points \((0,-7)\) and \((6, - 8)\) (or other points found using the same method) and then draw a straight line through them.

Answer:

To graph \(y =-\frac{1}{6}x - 7\), plot the y - intercept \((0,-7)\) and another point (e.g., \((6, - 8)\)) and draw a line through them.