Question

find the difference quotient for the function $p(x)=5x + 3$.
difference quotient:

Explanation:

Step1: Recall difference - quotient formula

The difference - quotient of a function $y = p(x)$ is given by $\frac{p(x + h)-p(x)}{h}$, where $h
eq0$.

Step2: Find $p(x + h)$

Given $p(x)=5x + 3$, then $p(x + h)=5(x + h)+3=5x+5h + 3$.

Step3: Substitute into the formula

$\frac{p(x + h)-p(x)}{h}=\frac{(5x + 5h+3)-(5x + 3)}{h}$.

Step4: Simplify the numerator

$(5x + 5h+3)-(5x + 3)=5x+5h + 3 - 5x - 3=5h$.

Step5: Simplify the fraction

$\frac{5h}{h}=5$.

Answer:

$5$