Question

what is the slope of the line that passes through the points (4,7) and (7,16)? write your answer in simplest form.

Explanation:

Step1: Recall the slope formula

The slope \( m \) of a line passing through 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 coordinates

Here, \( x_1 = 4 \), \( y_1 = 7 \), \( x_2 = 7 \), and \( y_2 = 16 \).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{16 - 7}{7 - 4} \).

Step4: Simplify the numerator and denominator

Simplify the numerator: \( 16 - 7 = 9 \). Simplify the denominator: \( 7 - 4 = 3 \). So, \( m=\frac{9}{3} \).

Step5: Reduce the fraction

\( \frac{9}{3}=3 \).

Answer:

The slope of the line is \( 3 \).