Question

a line intersects the points (8, -10) and (9, 4). what is the slope of this line in simplest form? m = ?

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Let \( (x_1, y_1)=(8, - 10) \) and \( (x_2, y_2)=(9, 4) \).

Step2: Substitute values into formula

Substitute \( x_1 = 8,y_1=-10,x_2 = 9,y_2 = 4 \) into the slope formula:
\( m=\frac{4-(-10)}{9 - 8} \)

Step3: Simplify numerator and denominator

Simplify the numerator: \( 4-(-10)=4 + 10=14 \)
Simplify the denominator: \( 9 - 8 = 1 \)
So \( m=\frac{14}{1}=14 \)

Answer:

14