Question

graph the line described by $y + 2 = \frac{5}{6}(x + 3)$. clear all draw:

Explanation:

Step1: Identify point from point-slope form

The equation $y + 2 = \frac{5}{6}(x + 3)$ is in point-slope form $y - y_1 = m(x - x_1)$, where $(x_1, y_1)=(-3, -2)$ and slope $m=\frac{5}{6}$.

Step2: Plot the first point

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

Step3: Use slope to find second point

Slope $\frac{5}{6}$ means $\frac{\text{rise}}{\text{run}}=\frac{5}{6}$. From $(-3, -2)$, move 6 units right to $x=-3+6=3$, then 5 units up to $y=-2+5=3$. This gives the second point $(3, 3)$.

Step4: Draw the line

Connect the points $(-3, -2)$ and $(3, 3)$ with a straight line, extending it across the grid.

Answer:

The line passes through points $(-3, -2)$ and $(3, 3)$, and extends infinitely in both directions on the coordinate grid.