Question

given $f(x)=x^{3}-5$, find the equation of the secant line passing through $(-3,f(-3))$ and $(2,f(2))$. write your answer in the form $y = mx + b$.

Explanation:

Step1: Calculate $f(-3)$ and $f(2)$

First, find $f(-3)$:

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Then, find $f(2)$:

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So the two points are $(-3,-32)$ and $(2,3)$.

Step2: Calculate the slope $m$

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Here, $x_1=-3,y_1 = - 32,x_2=2,y_2 = 3$.

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Step3: Find the y - intercept $b$

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(2,3)$ and $m = 7$.

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Answer:

$y = 7x-11$