Question

graph this line:
\\( y - 3 = -\frac{1}{2}(x + 6) \\)
click to select points on the graph.

Explanation:

Step1: Identify point from point-slope form

The equation $y - 3 = -\frac{1}{2}(x + 6)$ is in point-slope form $y-y_1=m(x-x_1)$, so one point is $(-6, 3)$.

Step2: Convert to slope-intercept form

Simplify to $y=mx+b$:
$y - 3 = -\frac{1}{2}x - 3$
$y = -\frac{1}{2}x$

Step3: Find y-intercept

When $x=0$, $y=0$, so the point is $(0, 0)$.

Step4: Find a third point

When $x=2$, $y = -\frac{1}{2}(2)=-1$, so the point is $(2, -1)$.

Answer:

Plot the points $(-6, 3)$, $(0, 0)$, and $(2, -1)$, then draw a straight line through them to graph the line $y = -\frac{1}{2}x$.