Question

student: find slope for line containing (a, 3) (-b, 1)

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the points

Let \((x_1, y_1)=(a, 2)\) and \((x_2, y_2)=(-b, 1)\).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m = \frac{1 - 2}{-b - a} \).

Step4: Simplify the expression

Simplify the numerator and denominator: \( m=\frac{-1}{- (a + b)}=\frac{1}{a + b} \).

Answer:

The slope of the line is \(\frac{1}{a + b}\)