# What is the slope intercept form of the line passing through (4,-9)  with a slope of 5/4 ?

Dec 20, 2015

$y = \frac{5}{4} x - 14$

#### Explanation:

The slope-intercept form of a line is written in the form:

$y = m x + b$

where:
$y =$y-coordinate
$m =$slope
$x =$x-coordinate
$b =$y-intercept

Since we do not know the value of $b$ yet, this is going to be what we are trying to solve for. We can do this by substituting the point, $\left(4 , - 9\right)$, and the slope, $\frac{5}{4}$, into an equation. The only unknown value will be $b$:

$y = m x + b$
$- 9 = \frac{5}{4} \left(4\right) + b$
$- 9 = \frac{5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} \left(\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}\right) + b$
$- 9 = 5 + b$
$- 14 = b$

Now that you know all your values, rewrite the equation in slope-intercept form:

$y = \frac{5}{4} x - 14$