# How do you graph 3x+4y=-10 using intercepts?

Jan 26, 2018

See a solution process below:

#### Explanation:

First, we will find the $x$ intercept by solve the equation for $y =$:

$3 x + \left(4 \cdot 0\right) = - 10$

$3 x + 0 = - 10$

$3 x = - 10$

$\left(3 x\right) / \textcolor{red}{3} = - \frac{10}{\textcolor{red}{3}}$

$x = - \frac{10}{3}$ or $\left(- \frac{10}{3} , 0\right)$

Next, we will find the $y$ intercept by solve the equation for $x =$:

$\left(3 \times 0\right) + 4 y = - 10$

$0 + 4 y = - 10$

$4 y = - 10$

$\left(4 y\right) / \textcolor{red}{4} = - \frac{10}{\textcolor{red}{4}}$

$y = - \frac{5}{2}$ or $\left(0 , - \frac{5}{2}\right)$

We can then plot the two intercepts on the coordinate plane:

graph{(x^2+(y+(5/2))^2-0.025)((x+(10/3))^2+y^2-0.025)=0 [-10, 10, -5, 5]}

Now, we can draw a straight line through the two points to graph the line:

graph{(3x + 4y + 10)(x^2+(y+(5/2))^2-0.025)((x+(10/3))^2+y^2-0.025)=0 [-10, 10, -5, 5]}