Question

section 2-2: point-slope form
graph the linear equation in point-slope

1. $y - 1 = -\frac{1}{2}(x + 3)$

$m = -\frac{1}{2}, x=-3, y = 1$
$(-3,1)$

Explanation:

Step1: Identify point and slope

The point - slope form is $y - y_1=m(x - x_1)$. For the equation $y - 1=-\frac{1}{2}(x + 3)$, we have the point $(x_1,y_1)=(-3,1)$ and slope $m =-\frac{1}{2}$.

Step2: Plot the point

Plot the point $(-3,1)$ on the coordinate - plane.

Step3: Use slope to find another point

The slope $m =-\frac{1}{2}=\frac{\text{rise}}{\text{run}}$. From the point $(-3,1)$, move 2 units to the right (run = 2) and 1 unit down (rise=-1) to get to the point $(-3 + 2,1-1)=( - 1,0)$.

Step4: Draw the line

Draw a straight line passing through the points $(-3,1)$ and $(-1,0)$.

Answer:

The graph is a straight line passing through the points $(-3,1)$ and $(-1,0)$.