How do you find the x and y intercept of 3 = 7x + -5y ?

Apr 19, 2017

See the entire solution process below:

Explanation:

To find the $x$ and $y$ intercept you substitute $0$ for one of the variables and solve for the other variable.

x-intercept:

Substitute $0$ for $y$ and solve for $x$

$3 = 7 x + \left(- 5 \cdot 0\right)$

$3 = 7 x + 0$

$3 = 7 x$

$\frac{3}{\textcolor{red}{7}} = \frac{7 x}{\textcolor{red}{7}}$

$\frac{3}{7} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} x}{\cancel{\textcolor{red}{7}}}$

$\frac{3}{7} = x$

The x-intercept is: $\frac{3}{7}$ or $\left(\frac{3}{7} , 0\right)$

y-intercept:

Substitute $0$ for $x$ and solve for $y$

$3 = \left(7 \cdot 0\right) + - 5 y$

$3 = 0 - 5 y$

$3 = - 5 y$

$\frac{3}{\textcolor{red}{- 5}} = \frac{- 5 y}{\textcolor{red}{- 5}}$

$\frac{3}{-} 5 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}} y}{\cancel{\textcolor{red}{- 5}}}$

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

The y-intercept is: $- \frac{3}{5}$ or $\left(0 , - \frac{3}{5}\right)$