Question

b-54: find the equation of the line with x - intercept (-4, 0) and y - intercept (0, 9)

Explanation:

Step1: Find the slope

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, $(x_1,y_1)=(-4,0)$ and $(x_2,y_2)=(0,9)$. So $m=\frac{9 - 0}{0-(-4)}=\frac{9}{4}$.

Step2: Use the slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know $m=\frac{9}{4}$ and the y - intercept $b = 9$. So the equation of the line is $y=\frac{9}{4}x+9$.

Answer:

$y=\frac{9}{4}x + 9$