Question

a line with a slope of \\(\frac{1}{3}\\) passes through the points (8, 8) and (u, 7). what is the value of u?
\\(u = \boxed{}\\)

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, \( m = \frac{1}{3} \), \( (x_1, y_1)=(8, 8) \), \( (x_2, y_2)=(u, 7) \).

Step2: Substitute into formula

Substitute values into the slope formula: \( \frac{1}{3}=\frac{7 - 8}{u - 8} \). Simplify the numerator: \( \frac{1}{3}=\frac{- 1}{u - 8} \).

Step3: Solve for \( u \)

Cross - multiply: \( 1\times(u - 8)=3\times(-1) \). So, \( u - 8=-3 \). Add 8 to both sides: \( u=-3 + 8 \).

Answer:

\( u = 5 \)