Question

sketch the graph of each line.

1. $m = -\frac{2}{3}$ point: $(1, -1)$

Explanation:

Step1: Find line equation (point-slope)

Use $y-y_1=m(x-x_1)$:
$y - (-1) = -\frac{2}{3}(x - 1)$
Simplify to slope-intercept:
$y + 1 = -\frac{2}{3}x + \frac{2}{3}$
$y = -\frac{2}{3}x + \frac{2}{3} - 1$
$y = -\frac{2}{3}x - \frac{1}{3}$

Step2: Plot given point

Mark the point $(1, -1)$ on the grid.

Step3: Use slope for 2nd point

Slope $m=-\frac{2}{3}$ means $\frac{\Delta y}{\Delta x}=-\frac{2}{3}$. From $(1, -1)$, move 3 right ($x=1+3=4$) and 2 down ($y=-1-2=-3$) to get $(4, -3)$. Or move 3 left ($x=1-3=-2$) and 2 up ($y=-1+2=1$) to get $(-2, 1)$.

Step4: Draw the line

Connect the plotted points $(1, -1)$, $(4, -3)$, $(-2, 1)$ and extend the line across the grid.

Answer:

The line with equation $y = -\frac{2}{3}x - \frac{1}{3}$ is graphed by plotting $(1, -1)$, using the slope to find additional points, then connecting and extending the line.