Question

the equation of the line in point slope form is missing a number. what is the number?
y + 4 =? (x + 2)
options: 2, \frac{1}{2}, -\frac{1}{2}, -2

Explanation:

Step1: Recall point-slope form

Point-slope form: $y - y_1 = m(x - x_1)$, where $m$ is slope, $(x_1,y_1)$ is a point on the line.

Step2: Identify given point

From $y+4=?(x+2)$, rewrite as $y - (-4) = m(x - (-2))$. So the point is $(-2, -4)$.

Step3: Find second point on line

From the graph, the line passes through $(4, -1)$.

Step4: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-1 - (-4)}{4 - (-2)}=\frac{3}{6}=\frac{1}{2}$

Answer:

B. $\frac{1}{2}$