Question

x f(x)
-2 -200
0 0
2 200
4

slope
y-intercept
equation

Explanation:

Step1: Calculate the slope

Use slope formula $m=\frac{f(x_2)-f(x_1)}{x_2-x_1}$.
Take $(x_1,f(x_1))=(0,0)$ and $(x_2,f(x_2))=(2,200)$:
$m=\frac{200-0}{2-0}=100$

Step2: Identify y-intercept

The y-intercept is $f(0)$, which is given as $0$.

Step3: Write linear equation

Use slope-intercept form $f(x)=mx+b$, where $m=100$, $b=0$:
$f(x)=100x$

Step4: Find $f(4)$

Substitute $x=4$ into the equation:
$f(4)=100\times4=400$

Answer:

• $f(4)=400$
• Slope: $100$
• Y-intercept: $0$
• Equation: $f(x)=100x$