Question

graph the line with slope $-dfrac{2}{3}$ passing through the point $(3, -2).$

Explanation:

Step1: Recall slope definition

Slope $m = \frac{\text{rise}}{\text{run}} = -\frac{2}{3}$, so rise = -2, run = 3.

Step2: Plot given point

Mark the point $(3, -2)$ on the coordinate plane.

Step3: Find second point

From $(3, -2)$, move 3 units right (run) and 2 units down (rise):
$x = 3 + 3 = 6$, $y = -2 + (-2) = -4$.
So second point is $(6, -4)$.

Step4: Find third point (optional)

From $(3, -2)$, move 3 units left and 2 units up:
$x = 3 - 3 = 0$, $y = -2 + 2 = 0$.
Third point is $(0, 0)$.

Step5: Draw the line

Connect the points $(0,0)$, $(3,-2)$, $(6,-4)$ with a straight line.

Answer:

The line passes through points $(0,0)$, $(3,-2)$, and $(6,-4)$, forming a straight line with slope $-\frac{2}{3}$ on the coordinate plane.