Question

what is the slope of this line? simplify your answer and write it as a proper fraction, improper fraction, or integer. the graph has a coordinate plane with a line passing through (0, -12) and (36, -6).

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 two points

From the graph, we have the points \((0, - 12)\) and \((36, - 6)\). Let \((x_1,y_1)=(0,-12)\) and \((x_2,y_2)=(36,-6)\).

Step3: Substitute into the slope formula

Substitute the values into the formula: \( m=\frac{-6-(-12)}{36 - 0} \).
Simplify the numerator: \(-6-(-12)=-6 + 12 = 6\).
Simplify the denominator: \(36-0 = 36\).
So, \( m=\frac{6}{36} \).

Step4: Simplify the fraction

Simplify \(\frac{6}{36}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 6. \(\frac{6\div6}{36\div6}=\frac{1}{6}\).

Answer:

\(\frac{1}{6}\)