# What is the slope-intercept form of 3x+5y=1 ?

Mar 28, 2018

$3 x + 5 y = 1$ in slope-intercept form is $y = - \frac{3}{5} x + \frac{1}{5}$.

#### Explanation:

A linear equation in slope intercept form is: $y = m x + b$. The given equation is in standard form, $A x + B x = C$. To convert from the standard from to the slope-intercept form, solve the standard form for $y$.

$3 x + 5 y = 1$

Subtract $3 x$ from both sides.

$5 y = - 3 x + 1$

Divide both sides by $5$.

$y = - \frac{3}{5} x + \frac{1}{5}$

The graph below shows the graph of both equations, which you can see is the same.

graph{(3x+5y-1)(y+3/5x-1/5)=0 [-10, 10, -5, 5]}

Mar 28, 2018

$y = - \frac{3}{5} x + \frac{1}{5}$

#### Explanation:

First subtract $3 x$ from both sides, and you should have $5 y = - 3 x + 1$. You are almost there to slope-intercept form, the $5 y$ needs to be just $y$. Divide by 5 on both sides (Make sure you divide $- 3 x$ AND 1 by 5!). And then you have it in slope intercept form, $y = - \frac{3}{5} x + \frac{1}{5}$ .