# How do you write an equation in point-slope form for the line through the given slope:(4,-6); m=3/5?

Apr 7, 2015

Gradient ($m$)$= \frac{3}{5}$
Coordinates located on the line: $\left(4 , - 6\right)$
$4$ is the x-coordinate while $- 6$ is the y-coordinate

Remember the general linear equation of $y = m x + c$

We can use the method of substitution to find the y-intercept (c) in the linear equation first.
As we substitute the coordinates & gradient in the general linear equation of $y = m x + c$ ... We get:
$- 6 = \frac{3}{5}$x$4$$+ c$
$- 6 = \frac{12}{5}$$+ c$
$- 6 - \frac{12}{5} =$$c$
$- \frac{42}{5} =$$c$
$c = - \frac{42}{5} = - 8.4$

Now that we know the y-intercept (c) of the linear equation, we can form the linear equation by adding the gradient and y-intercept into the general equation of $y = m x + c$.

Thus, the linear equation would be $y = \frac{3}{5} x - 8.4$