Question

Graph the line passing through the given point with the given slope

$\text{(-2,2),-}\frac{1}{3}$

Short answer

The graph of the line passing through the point $(-2,2)$ with the slope $\frac{-1}{3}$ is

Step-by-step solution

Step-1 – Apply the concept of slope of a line

The slope of a line is the ratio of the change in the y-coordinates to the change in the x- coordinates.

Symbolically, the slope m of the line passing through the points $\left(x_1,y_1\right)\text{and}\left(x_2,y_2\right)$ is given by $m=\frac{y_2-y_1}{x_2-x_1}$ where $x_1\ne x_2$.

Step-2 – Plot the given ordered pair   

The given ordered pair is $\left(-2,2\right)$

Hence plot the point in the graph such that the point is 2 unit in the negative x-axis and 2 units in the positive y-axis.

Therefore, the point $\left(-2,2\right)$ in the graph is as shown below:

Step-3 – Find a new point using the slope

Since the slope is $-\frac{1}{3}$, go down 1 unit and 3 units to the right. Now, plot the new point at $\left(1,1\right)$.

Therefore the new point in the graph is given as below:

Step-3 – Graph the line

Draw a line containing the points $\left(-2,2\right)\text{and}\left(1,1\right)$. Therefore the graph is