Question

a line with a slope of $-\frac{1}{4}$ passes through the points $(p, -10)$ and $(-1, -9)$. what is the value of $p$?
$p = \square$
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Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( m = -\frac{1}{4} \), \( (x_1, y_1)=(p, - 10) \) and \( (x_2, y_2)=(-1, - 9) \).
So we substitute into the formula: \( -\frac{1}{4}=\frac{-9 - (-10)}{-1 - p} \)

Step2: Simplify the numerator

Simplify the numerator of the right - hand side: \( -9-(-10)=-9 + 10 = 1 \). So the equation becomes \( -\frac{1}{4}=\frac{1}{-1 - p} \)

Step3: Cross - multiply

Cross - multiply to get: \( -1\times(-1 - p)=4\times1 \)

Step4: Simplify the left - hand side

Simplify the left - hand side: \( 1 + p = 4 \)

Step5: Solve for \( p \)

Subtract 1 from both sides: \( p=4 - 1=3 \)

Answer:

\( p = 3 \)