Question

representing a graph with a slope- a function f(x) is graphed. what is the slope of the function? m = what is the y-intercept of the function? b = which equation represents the graph of the function?

Explanation:

Step1: Identify slope using two points

Choose points $(0,1)$ and $(1,3)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{3-1}{1-0}=2$

Step2: Find y-intercept

The y-intercept is where $x=0$, from graph it is $(0,1)$, so $b=1$.

Step3: Write slope-intercept equation

Slope-intercept form: $y=mx+b$
Substitute $m=2$, $b=1$: $y=2x+1$

Answer:

Slope: $m=2$
y-intercept: $b=1$
Equation: $y=2x+1$