# WeUsing the x-intercept and y-intercept, how do you graph 2x-3y=5?

Dec 4, 2016

graph{2x-3y=5 [-10, 10, -5, 5]}

$e q u a t i o n : y = \frac{2 x - 5}{3}$

#### Explanation:

the equation can be converted into $y = m x + c$:

$2 x - 3 y = 5$

(-2x)

$- 3 y = - 2 x + 5$

(/3)

$- y = \frac{- 2 x + 5}{3}$

(*-1)

$y = - \frac{- 2 x + 5}{3}$

$y = \frac{2 x - 5}{3}$

Dec 4, 2016

$\text{Plot the points " (0,-5/3)" and } \left(\frac{5}{2} , 0\right)$

#### Explanation:

When the line with given equation crosses the y-axis the corresponding x-coordinate at this point will be zero.
Substituting x = 0 into the equation gives the y-intercept.

$\left(2 \times 0\right) - 3 y = 5 \Rightarrow - 3 y = 5 \Rightarrow y = - \frac{5}{3}$

$\Rightarrow \left(0 , - \frac{5}{3}\right) \text{ is the point on the y-axis}$

Similarly when the line crosses the x-axis the corresponding
y-coordinate at this point will be zero. Substituting y = 0 into the equation gives the x-intercept.

$2 x - \left(3 \times 0\right) = 5 \Rightarrow 2 x = 5 \Rightarrow x = \frac{5}{2}$

$\Rightarrow \left(\frac{5}{2} , 0\right) \text{ is the point on the x-axis}$

Plot these 2 points and draw a straight line through them.
graph{2/3x-5/3 [-10, 10, -5, 5]}