# How do you find the x and y intercepts for 5x -2y -6 =0?

x-intercept $\left(\frac{6}{5} , 0\right)$
y-intercept $\left(0 , - 3\right)$

#### Explanation:

The way to find intercepts is simple. All we need to do is first set one variable to zero. Let say we start with $y = 0$ then solve for the x-intercept. After which, set $x = 0$ then solve for y-intercept.

Let us do it.

$5 x - 2 y - 6 = 0$

Set $y = 0$ from the original equation

$5 x - 2 y - 6 = 0$

$5 x - 2 \left(0\right) - 6 = 0$

$5 x - 0 - 6 = 0$

$5 x = 6$

$\frac{5 x}{5} = \frac{6}{5}$

$\frac{\cancel{5} x}{\cancel{5}} = \frac{6}{5}$

$x = \frac{6}{5} = 1.2$

Now, Set $x = 0$ in the original equation $5 x - 2 y - 6 = 0$

$5 \left(0\right) - 2 y - 6 = 0$

$0 - 2 y - 6 = 0$
$- 2 y = 6$

$\frac{- 2 y}{- 2} = \frac{6}{- 2}$

$\frac{\cancel{- 2} y}{\cancel{- 2}} = \frac{6}{- 2}$

$y = \frac{6}{- 2}$

$y = - 3$

Kindly see the graph of $5 x - 2 y - 6 = 0$
We can see that the line intersects with the axes at (6/5, 0) and (0, -3)#

graph{5x-2y-6=0[-20,20,-10,10]}

God bless....I hope the explanation is useful.