# How do you graph y=-5x+10 using intercepts?

Sep 28, 2017

See a solution process below:

#### Explanation:

First, find the $y$-intercept by setting $x$ to $0$ and calculating $y$:

y-intercept:

$y = \left(- 5 \cdot 0\right) + 10$

$y = 0 + 10$

$y = 10$ or $\left(0 , 10\right)$

Next, find the $x$-intercept by setting $y$ to $0$ and solving for $x$:

x-intercept:

$0 = - 5 x + 10$

$0 - \textcolor{red}{10} = - 5 x + 10 - \textcolor{red}{10}$

$- 10 = - 5 x + 0$

$- 10 = - 5 x$

$\frac{- 10}{\textcolor{red}{- 5}} = \frac{- 5 x}{\textcolor{red}{- 5}}$

$2 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}} x}{\cancel{\textcolor{red}{- 5}}}$

$2 = x$

$x = 2$ or $\left(2 , 0\right)$

We can next graph the two points on the coordinate plane:

graph{(x^2+(y-10)^2-0.125)((x-2)^2+y^2-0.125)=0 [-25, 25, -12.5, 12.5]}

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

graph{(y+5x-10)(x^2+(y-10)^2-0.125)((x-2)^2+y^2-0.125)=0 [-25, 25, -12.5, 12.5]}