Question

a line with a slope of \\(\frac{1}{8}\\) passes through the points (8, -3) and (j, -4). what is the value of j?
j =

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, \( m = \frac{1}{8} \), \( (x_1, y_1)=(8, - 3) \), \( (x_2, y_2)=(j, - 4) \).

Step2: Substitute values into formula

Substitute into the slope formula: \( \frac{1}{8}=\frac{-4 - (-3)}{j - 8} \). Simplify the numerator: \( -4-(-3)=-4 + 3=-1 \). So the equation becomes \( \frac{1}{8}=\frac{-1}{j - 8} \).

Step3: Cross - multiply to solve for \( j \)

Cross - multiplying gives \( 1\times(j - 8)=8\times(-1) \). Which simplifies to \( j-8=-8 \).

Step4: Solve for \( j \)

Add 8 to both sides of the equation: \( j-8 + 8=-8 + 8 \), so \( j = 0 \).

Answer:

\( j = 0 \)