Question

a line intersects the points (1, 7) and (2, 10). 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 given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify coordinates

Let \((x_1, y_1)=(1, 7)\) and \((x_2, y_2)=(2, 10)\).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{10 - 7}{2 - 1} \).

Step4: Simplify the expression

Calculate the numerator and denominator: \( 10 - 7 = 3 \) and \( 2 - 1 = 1 \), so \( m=\frac{3}{1}=3 \).

Answer:

\( 3 \)