find the equation of the line. use exact numbers. y= x+

Explanation:

Step1: Find the slope

The line passes through points $(0, 3)$ and $(- 2,0)$. The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1=3,x_2=-2,y_2 = 0$. So $m=\frac{0 - 3}{-2-0}=\frac{3}{2}$.

Step2: Find the y - intercept

The y - intercept $b$ is the y - coordinate of the point where the line crosses the y - axis. The line crosses the y - axis at $(0,3)$, so $b = 3$.

Step3: Write the equation of the line

The slope - intercept form of a line is $y=mx + b$. Substituting $m=\frac{3}{2}$ and $b = 3$ into the equation, we get $y=\frac{3}{2}x+3$.

Answer:

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