Question

find an equation for the line below.
y = \frac{3}{2}x+

Explanation:

Step1: Identify two points

Let the points be $(-4, - 3)$ and $(0,6)$.

Step2: Calculate the slope

The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{6-(-3)}{0 - (-4)}=\frac{9}{4}$. But from the given form $y=\frac{3}{2}x + b$, we'll use the point - slope form with the point $(0,6)$ (y - intercept form is easier here). The general form of a line is $y=mx + b$, where $m$ is slope and $b$ is y - intercept. We know $m = \frac{3}{2}$, and using the point $(0,6)$ (when $x = 0,y=6$), substituting into $y=\frac{3}{2}x + b$ gives $6=\frac{3}{2}(0)+b$.

Step3: Solve for b

$b = 6$.

Answer:

$y=\frac{3}{2}x + 6$