Question

graph the line with slope $\frac{1}{2}$ passing through the point $(-2, 2)$.

Explanation:

Step1: Find line equation (point-slope)

Point-slope formula: $y - y_1 = m(x - x_1)$
Substitute $m=\frac{1}{2}$, $x_1=-2$, $y_1=2$:
$y - 2 = \frac{1}{2}(x - (-2))$

Step2: Simplify to slope-intercept form

Simplify the right-hand side:
$y - 2 = \frac{1}{2}(x + 2)$
$y - 2 = \frac{1}{2}x + 1$
Add 2 to both sides:
$y = \frac{1}{2}x + 3$

Step3: Identify a second point

Use slope $\frac{1}{2}=\frac{\Delta y}{\Delta x}$: from $(-2,2)$, move 2 right ($\Delta x=2$) and 1 up ($\Delta y=1$) to get $(0,3)$.

Step4: Plot and connect points

Mark $(-2,2)$ and $(0,3)$, draw a straight line through them, extending across the grid.

Answer:

The line $y = \frac{1}{2}x + 3$, passing through $(-2,2)$ and $(0,3)$, graphed on the coordinate grid.