Question

Write an equation of the slope intercept form, of the line with an $x$-intercept at $(3,0)$ and a $y$-intercept at $(0,-5)$

• A. $y=\frac{4}{3}x-3$
• B. $y=\frac{5}{3}x-5$
• C. $y=6x-5$
• D. $y=\frac{1}{2}x-5$

Answer 1

Answer: (B)

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

Since slope of line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

We now find the slope of the line passing through the points $(3,0)$ and $(0,-5)$ as shown below:

$m=\frac{-5-0}{0-3}=\frac{5}{3}$

Therefore, the slope of the line is $\frac{5}{3}$.

Now use the slope and either of the two points to find the $y$-intercept.

$y=mx+b$

$0=\frac{5}{3}\left(3\right)+b$

$b=-5$

Write the equation in slope intercept form as:

$y=mx+b$

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

Hence, the equation of the line is $y=\frac{5}{3}x-5$.