# How do you write the equation of a line that passes through (4,-3) and has a slope of -3/4?

Dec 3, 2016

$y = - \frac{3}{4} x$

#### Explanation:

$y = m x + b$

where:
$m =$ slope of the line
$b =$ y-intercept

the slope is already given ($- \frac{3}{4}$).
All that remains is to find the y-intercept.

To find the y-intercept, we use the coordinates of a point which we know lies on the line. Such a point was also given $\left(4 , - 3\right)$.

$y = - \frac{3}{4} x + b$

$\implies - 3 = - \frac{3}{4} \left(4\right) + b$

$\implies - 3 = - 3 + b$
$\implies b = 0$

Since the y-intercept is 0, the equation of the line is

$y = - \frac{3}{4} x$