# How do you find the slope and intercept of 7x + 3y=4?

$- \frac{7}{3}$ & $\frac{4}{3}$

#### Explanation:

Given that

$7 x + 3 y = 4$

$3 y = - 7 x + 4$

$y = - \frac{7}{3} x + \frac{4}{3}$

Comparing above equation with the slope-intercept form of straight line: $y = m x + c$ we get

Slope: $m = - \frac{7}{3}$

y-Intercept: $c = \frac{4}{3}$

Jul 6, 2018

Slope= $- \frac{7}{3}$

$y$-intercept= $\frac{4}{3}$

#### Explanation:

We can find the $y$-intercept by setting $x$ to zero, because that is exactly what the $y$-intercept means...when $x = 0$ we are on the $y$ axis.

If we set $x$ to zero, that term disappears, and we are left with

$3 y = 4 \implies y = \frac{4}{3}$

This is our $y$-intercept.

To go about finding our slope, we can convert this equation into slope-intercept form

$y = m x + b$ where $m$ is the slope and $b$ is the $y$-intercept.

$7 x + 3 y = 4$

We want just a $y$ on the left, so we can subtract $7 x$ from both sides to get

$3 y = - 7 x + 4$

Dividing all terms by $3$, we get

$y = - \frac{7}{3} x + \frac{4}{3}$

Our slope is the coefficient on $x$, which in our case, is $- \frac{7}{3}$.

The $y$-intercept is the constant and we see that this is $\frac{4}{3}$.

Hope this helps!