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 slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the two points

We have the points \((-4, 3)\) and \((0, -3)\). Let \((x_1, y_1) = (-4, 3)\) and \((x_2, y_2) = (0, -3)\).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m = \frac{-3 - 3}{0 - (-4)} \).

Step4: Simplify the numerator and denominator

Simplify the numerator: \(-3 - 3 = -6\). Simplify the denominator: \(0 - (-4) = 0 + 4 = 4\). So \( m = \frac{-6}{4} \).

Step5: Reduce the fraction

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

Answer:

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