Question

what is the slope of this line? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Identify two points on the line

We can see that the line passes through the origin \((0,0)\) and another point, for example, when \(x = 32\), \(y=-8\) (or we can use \((-32,8)\) and \((0,0)\)). Let's use \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(32, - 8)\).

Step2: Use the slope formula

The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting the values: \(m=\frac{-8 - 0}{32-0}=\frac{-8}{32}\)

Step3: Simplify the fraction

Simplify \(\frac{-8}{32}\) by dividing numerator and denominator by their greatest common divisor, which is 8. \(\frac{-8\div8}{32\div8}=\frac{-1}{4}\)

Answer:

\(-\frac{1}{4}\)