Hey!
The first step to solving this problem would be to graph the equation. Since this equation is obviously a linear equation, once it is graph it should have to points. One point will be graph on the [tex]x[/tex] axis, and another on the [tex]y[/tex] axis. If you don't know how to solve graph this equation, let me show you how its done.
Alright, let's start with our non changed equation.
Original Equation :
5x - 2y = 20
Now, since we want to find two different points we're going to write two different equations.
I'm going to start you off with the first equation. This first equation will solve the [tex]x[/tex] - intercept point.
[tex]X[/tex] - Intercept Equation :
5x - 2 ( 0 ) = 20
Notice how in the equation I replaced [tex]y[/tex] with zero. I do this so that it will be easier to remove [tex]y[/tex] all together. We want to remove [tex]y[/tex] so we can find [tex]x[/tex].
So, now we'll solve the [tex]x[/tex] - intercept equation.
The first step to solving the equation would be to multiply -2 by zero, to get rid of [tex]y[/tex].
Original [tex]X[/tex] - Intercept Equation :
5x - 2 ( 0 ) = 20
New [tex]X[/tex] - Intercept Equation {Changed by Multiplying -2 by 0} :
5x = 20
Next, we'd divide both sides of the equation by 5, so as to get [tex]x[/tex] on its own. We can basically call this simplification since we are simplifying the equation further than it already is. This will final answer will give us the [tex]x[/tex] - intercept.
Old [tex]X[/tex] - Intercept Equation :
5x = 20
New [tex]X[/tex] - Intercept Equation {Changed by Simplification} :
x = 4
Great! So now we know the [tex]x[/tex] - intercept which is ( 4, 0 ).
Moving on the writing our second equation, which will solve for our [tex]y[/tex] - intercept.
[tex]Y[/tex] - Intercept Equation :
5 ( 0 ) - 2y = 20
Again I replaced [tex]x[/tex] with zero for the same reason just this time to get [tex]y[/tex] on its own.
So now we'll solve the [tex]y[/tex] - intercept equation.
The first step to solving the equation would be to multiply 5 by zero, to get rid of [tex]x[/tex].
Original [tex]Y[/tex] - Intercept Equation :
5 ( 0 ) - 2y = 20
New [tex]Y[/tex] - Intercept Equation {Changed by Multiplying 5 by 0} :
-2y = 20
Next, we'd divide both sides of the equation by -2, so as to get [tex]y[/tex] on its own. We can basically call this simplification since we are simplifying the equation further than it already is. This will final answer will give us the [tex]y[/tex] - intercept.
Old [tex]Y[/tex] - Intercept Equation :
-2y = 20
New [tex]Y[/tex] - Intercept Equation {Changed by Simplification} :
y = -10
Awesome! So now we know the [tex]y[/tex] - intercept which is ( 0, -10 ).
Alright! We've successfully solved both intercepts for the equation. Take a look at the picture below if you want to see what those intercepts would look like on a graph.
So, the [tex]x[/tex] and [tex]y[/tex] intercepts of the equation 5x - 2y = 20 are ( 4, 0 ) and ( 0, -10 ).
Hope that helps!
- Lindsey Frazier ♥
