# What is the slope-intercept form of 13x+2y=12 ?

Dec 30, 2015

The equation of a line represented in the form $y = m x + b$ is known as the slope-intercept form. Step by step working is shown to get the solution.

#### Explanation:

The given equation is $13 x + 2 y = 12$
To get this into the form $y = m x + b$
$m$ is the slope and $b$ is the $y$-intercept.

Solve the given equation for $y$ and we would get what we wanted.

$13 x + 2 y = 12$
Subtract $13 x$ from both the sides. This is done to get $y$ term all alone on the left side of the equation.

$13 x + 2 y - 13 x = 12 - 13 x$
$2 y = 12 - 13 x$

We still have a $2$ which is multiplied with $y$ and we want $y$ isolated. For this, we shall use the opposite operation of multiplication which is division.

The next step is to divide both sides by $2$

$\frac{2 y}{2} = \frac{12}{2} - \frac{13 x}{2}$

$y = 6 - \frac{13}{2} x$

Let us rewrite this in the form $y = m x + b$

$y = - \frac{13}{2} x + 6$ This is the slope-intercept form of the line.