Question

what is the rate of change of y with respect to x for this function? a $\frac{1}{4}$

Explanation:

Step1: Recall the rate of change formula

The rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Let \((x_1, y_1)=(-15, -3)\) and \((x_2, y_2)=(-7, -1)\).

Step2: Substitute the values into the formula

Substitute \(x_1=-15\), \(y_1 = - 3\), \(x_2=-7\), and \(y_2=-1\) into the slope formula:
\(m=\frac{-1-(-3)}{-7 - (-15)}\)

Step3: Simplify the numerator and denominator

Simplify the numerator: \(-1-(-3)=-1 + 3=2\)
Simplify the denominator: \(-7-(-15)=-7 + 15 = 8\)

Step4: Calculate the slope

\(m=\frac{2}{8}=\frac{1}{4}\)

Answer:

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