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 formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1,y_1)\) and \((x_2,y_2)\) are two points on the line.

Step2: Identify the points

Here, \((x_1,y_1)=(-2,1)\) and \((x_2,y_2)=(2,7)\).

Step3: Substitute into the formula

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

Step4: Simplify 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:

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