Question

find an equation of the line graphed below. write your answer in the slope - intercept form y = mx + b. y = question help: video message instructor

Explanation:

Step1: Find two points on the line

The line passes through points $(0, 2)$ and $(1, 5)$.

Step2: Calculate the slope $m$

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

Step3: Find the y - intercept $b$

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

Step4: Write the equation of the line

Substitute $m = 3$ and $b=2$ into $y=mx + b$. We get $y = 3x+2$.

Answer:

$y = 3x + 2$