Question

a line that includes the points $(-3, -2)$ and $(1, c)$ has a slope of $\frac{1}{2}$. what is the value of $c$?
$c = \square$
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Explanation:

Step1: Recall slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$.

Step2: Substitute given values

Let $(x_1,y_1)=(-3,-2)$, $(x_2,y_2)=(1,c)$, and $m=\frac{1}{2}$.
$\frac{1}{2}=\frac{c-(-2)}{1-(-3)}$

Step3: Simplify denominator

Calculate $1-(-3)=4$, so:
$\frac{1}{2}=\frac{c+2}{4}$

Step4: Solve for $c$

Multiply both sides by 4: $4\times\frac{1}{2}=c+2$
Simplify left side: $2=c+2$
Subtract 2 from both sides: $c=2-2$

Answer:

$c=0$