# How do you graph 3x-5y=15 using intercepts?

Aug 2, 2017

See a solution process below:

#### Explanation:

To find the intercepts, equate one variable to $0$ and solve for the other variable:

y-intercept

Set $x$ to $0$ and solve for $y$ giving:

$3 x - 5 y = 15$ becomes:

$\left(3 \cdot 0\right) - 5 y = 15$

$0 - 5 y = 15$

$- 5 y = 15$

$\frac{- 5 y}{\textcolor{red}{- 5}} = \frac{15}{\textcolor{red}{- 5}}$

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

$y = - 3$ or $\left(0 , - 3\right)$

x-intercept

Set $y$ to $0$ and solve for $x$ giving:

$3 x - 5 y = 15$ becomes:

$3 x - \left(5 \cdot 0\right) = 15$

$3 x - 0 = 15$

$3 x = 15$

$\frac{3 x}{\textcolor{red}{3}} = \frac{15}{\textcolor{red}{3}}$

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

$x = 5$ or $\left(5 , 0\right)$

Next. we can plot the two points on the grid:

graph{((x-5)^2+(y)^2-0.125)((x)^2+(y+3)^2-0.125)=0 [-20, 20, -10, 10]}

Then, draw a line through the two points:

graph{(3x - 5y -15)((x-5)^2+(y)^2-0.125)((x)^2+(y+3)^2-0.125)=0 [-20, 20, -10, 10]}

Aug 2, 2017

Draw a straight line through the intercept points as indicated below.

#### Explanation:

Note that the given equation: $3 x - 5 y = 15$ is a linear (straight line) equation with:
$x$-intercept (value of $x$ when $y = 0$) of $x = 5$
and
$y$-intercept (value of $y$ when $x = 0$) of $y = - 3$

Therefore we have the two points:
$\textcolor{w h i t e}{\text{XXX}} \left({x}_{1} , {y}_{1}\right) = \left(5 , 0\right) \mathmr{and} \left({x}_{2} , {y}_{2}\right) = \left(0 , - 3\right)$

Plotting these two points on the Cartesian plane and drawing a straight line through them should give a graph that looks like: 