Question

a line that includes the points (8, q) and (4, 1) has a slope of $-\frac{7}{4}$. what is the value of q?
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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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( (x_1,y_1)=(8,q) \), \( (x_2,y_2)=(4,1) \), and \( m = -\frac{7}{4} \).

Step2: Substitute values into formula

Substitute into the slope formula: \( -\frac{7}{4}=\frac{1 - q}{4 - 8} \). Simplify the denominator: \( 4 - 8=-4 \), so the equation becomes \( -\frac{7}{4}=\frac{1 - q}{-4} \).

Step3: Solve for \( q \)

Multiply both sides by \( - 4 \): \( -\frac{7}{4}\times(-4)=1 - q \). The left side simplifies to \( 7 = 1 - q \). Subtract 1 from both sides: \( 7-1=-q \), so \( 6=-q \). Multiply both sides by \( - 1 \): \( q=-6 \).

Answer:

\( -6 \)