# How do you find the slope and y intercept of 3x +4y = 5?

Apr 29, 2018

Slope: $- \frac{3}{4}$
$y$-intercept: $\left(0 , \frac{5}{4}\right)$

#### Explanation:

To find the slope of a standard equation, we need to make $y$ by itself.

$3 x + 4 y = 5$

First, subtract $\textcolor{red}{3 x}$ from both sides of the equation:
$3 x + 4 y \quad \textcolor{red}{- \quad 3 x} = 5 \quad \textcolor{red}{- \quad 3 x}$

$4 y = 5 - 3 x$

Divide both sides by $\textcolor{red}{4}$:
$\frac{4 y}{\textcolor{red}{4}} = \frac{5 - 3 x}{\textcolor{red}{4}}$

$y = \frac{5}{4} - \frac{3 x}{4}$

The slope is the value multiplying the $x$, so the slope is $- \frac{3}{4}$.

$- - - - - - - - - - - - - - - - - - - -$

To find the $y$-intercept, we set $x$ to be $0$ and find the value of $y$:
$y = \frac{5}{4} - \frac{3 x}{4}$

$y = \frac{5}{4} - \frac{3 \left(0\right)}{4}$

Simplify:
$y = \frac{5}{4} - 0$

$y = \frac{5}{4}$

So the $y$-intercept is at $\left(0 , \frac{5}{4}\right)$.

Hope this helps!