Question

a line that includes the points (c, 4) and (4, 5) has a slope of \\(\frac{1}{9}\\). 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 $(x_1,y_1)=(c,4)$, $(x_2,y_2)=(4,5)$, and $m=\frac{1}{9}$.
$\frac{1}{9}=\frac{5-4}{4-c}$

Step3: Simplify and solve for $c$

First simplify numerator: $\frac{1}{9}=\frac{1}{4-c}$
Cross-multiply: $4-c=9$
Solve for $c$: $c=4-9=-5$

Answer:

$c=-5$