Question

find the slope - intercept form equation of the line graphed below.

Explanation:

Step1: Identify two points

Let's take two points on the line: $(0, 2)$ and $(1,5)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(0,2)$ and $(x_2,y_2)=(1,5)$ gives $m=\frac{5 - 2}{1-0}=3$.

Step3: Identify the y - intercept $b$

The y - intercept is the y - value when $x = 0$. From the point $(0,2)$, $b = 2$.

Step4: Write the slope - intercept form

The slope - intercept form of a line is $y=mx + b$. Substituting $m = 3$ and $b=2$ gives $y = 3x+2$.

Answer:

$y = 3x + 2$