Question

what is the slope of this line?
(-3, 4)
(3, -4)

Explanation:

Step1: Recall 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 points

We have two points: \((-3, 4)\) and \((3, -4)\). Let \((x_1, y_1)=(-3, 4)\) and \((x_2, y_2)=(3, -4)\).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{-4 - 4}{3 - (-3)} \).

Step4: Simplify the numerator and denominator

Simplify the numerator: \(-4 - 4=-8\). Simplify the denominator: \(3 - (-3)=3 + 3 = 6\). So \( m=\frac{-8}{6} \).

Step5: Reduce the fraction

Reduce \(\frac{-8}{6}\) by dividing numerator and denominator by their greatest common divisor, which is 2. We get \( m =-\frac{4}{3} \).

Answer:

\(-\frac{4}{3}\)