Question

using the slope formula, find the slope of the line through the given points. (9,2) and (4,7) what is the slope of the line? select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the slope of the line is (type an integer or a simplified fraction.) b. the slope of the line is undefined.

Explanation:

Step1: Recall slope formula

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

Step2: Identify coordinates

Let \((x_1, y_1)=(9, 2)\) and \((x_2, y_2)=(4, 7)\).

Step3: Substitute into formula

Substitute the values into the slope formula: \(m=\frac{7 - 2}{4 - 9}\).

Step4: Simplify numerator and denominator

Simplify the numerator: \(7 - 2 = 5\). Simplify the denominator: \(4 - 9=-5\). So \(m=\frac{5}{-5}\).

Step5: Simplify the fraction

Simplify \(\frac{5}{-5}=-1\).

Answer:

A. The slope of the line is \(-1\)