# How do you graph -10x+15y=60 using intercepts?

Aug 19, 2017

See a solution process below:

#### Explanation:

x-intercept

To find the $x$-intercept we set $y$ to $0$ and solve for $x$:

$- 10 x + \left(15 \cdot 0\right) = 60$

$- 10 x + 0 = 60$

$- 10 x = 60$

$\frac{- 10 x}{\textcolor{red}{- 10}} = \frac{60}{\textcolor{red}{- 10}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 10}}} x}{\cancel{\textcolor{red}{- 10}}} = - 6$

$x = - 6$ or $\left(- 6 , 0\right)$

y-intercept

To find the $y$-intercept we set $x$ to $0$ and solve for $y$:

$\left(- 10 \times 0\right) + 15 y = 60$

$0 + 15 y = 60$

$15 y = 60$

$\frac{15 y}{\textcolor{red}{15}} = \frac{60}{\textcolor{red}{15}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{15}}} y}{\cancel{\textcolor{red}{15}}} = 4$

$y = 4$ or $\left(0 , 4\right)$

We can now plot the two points and draw a line through them to graph the equation:

graph{((x+6)^2+y^2-0.025)(x^2+(y-4)^2-0.025)(-10x+15y-60)=0}