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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Let \((x_1, y_1)=(-2, 1)\) and \((x_2, y_2)=(2, 7)\).

Step2: Substitute the values into the formula

Substitute \( x_1=-2 \), \( y_1 = 1 \), \( x_2=2 \), and \( y_2 = 7 \) into the slope formula:
\( m=\frac{7 - 1}{2-(-2)} \)

Step3: Simplify the numerator and denominator

Simplify the numerator: \( 7 - 1=6 \)
Simplify the denominator: \( 2-(-2)=2 + 2 = 4 \)
So, \( m=\frac{6}{4} \)

Step4: Reduce the fraction

Simplify \(\frac{6}{4}\) by dividing both the numerator and denominator by their greatest common divisor, which is 2:
\( \frac{6\div2}{4\div2}=\frac{3}{2} \)

Answer:

\(\frac{3}{2}\)