Question

write the equation of the line in fully simplified slope - intercept form.

Explanation:

Step1: Identify two points on the line

Let's take two clear - cut points on the line. Suppose the points are $(-5,0)$ and $(0, - 3)$.

Step2: Calculate the slope $m$

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

Step3: Identify the y - intercept $b$

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

Step4: Write the equation in slope - intercept form

The slope - intercept form of a line is $y = mx + b$. Substituting $m =-\frac{3}{5}$ and $b=-3$ into the equation, we get $y=-\frac{3}{5}x - 3$.

Answer:

$y =-\frac{3}{5}x - 3$