Question

what is the slope of this line? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall the 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 two points

We have the points \( (2, 2) \) and \( (4, 7) \). Let \( (x_1, y_1)=(2, 2) \) and \( (x_2, y_2)=(4, 7) \).

Step3: Substitute into the slope formula

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

Step4: Simplify the expression

Simplify the numerator and the denominator: \( 7 - 2 = 5 \) and \( 4 - 2 = 2 \), so \( m=\frac{5}{2} \).

Answer:

\(\frac{5}{2}\)