How do you graph 4x=2y+6 using the x and y intercepts?

1 Answer
Nov 9, 2017

See a solution process below:

Explanation:

First, we need to determine the x and y intercepts.

x-intercept

Set y equal to 0 and solve for x:

4x = (2 * 0) + 6

4x = 0 + 6

4x = 6

(4x)/color(red)(4) = 6/color(red)(4)

(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 3/2

x = 3/2

(3/2, 0)

x-intercept

Set x equal to 0 and solve for y:

4 * 0 = 2y + 6

0 = 2y + 6

0 - color(red)(6) = 2y + 6 - color(red)(6)

-6 = 2y + 0

-6 = 2y

-6/color(red)(2) = (2y)/color(red)(2)

-3 = (color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2))

-3 = y

(0, -3)

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

graph{(x^2+(y+3)^2-0.025)((x-(3/2))^2+y^2-0.025)=0 [-10, 10, -5, 5]}

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

graph{(4x-2y-6)(x^2+(y+3)^2-0.025)((x-(3/2))^2+y^2-0.025)=0 [-10, 10, -5, 5]}