how do I solve 6x+2y=10 and turn that into a coordinate pair?

Question

I am doing my math homework and I am given an equation which is 6x+2y=10. I have to solve it and then I am given a part of a coordinate pair which is (__,-4). I have to fill the X coordinate and graph it. How do I do this?

Answer 1

As a general rule, to solve "something" in Math is to find the unknowns, given some assumptions !

 

Here the answer, as a pair of coordinates, is  { x  ;  y =(10 - 6x)/2 }

 

( x  ;  y=5-3x )

 

For the second part of the problem, we're given y = -4 . We use this information to find the corresponding x .

 

-4 = 5 - 3x -------> 3x = 5 + 4 -------> x = 3 .

 

Therefore, the pair is ( 3 ; -4 ) . To graph this linear function we use an easy second point (0 ; 5) in conjunction with the already found (3 ; -4) . 

Answer 2

Your original equation is a linear equation, meaning it's a straight line.  You have no "solution", as each x point will give a unique y point.  You are however given a y point of -4.  Simply plug that into your equation, and solve for the corresponding x point.

 

• 6x+2(-4)=10
• 6x-8=10
• 6x=18    add 8 to each side
• x=3        divide both sides by 6
• Your point is (3,-4)

 

If you need to graph the entire line, you can find the x and y intercepts as shown below.  If you only need to graph the point (3,-4), simply go over 3 in the x direction (to the right), and then down 4 in the y direction.

 

 

To graph the entire line:

• x intercept is where y=0
• 6x+2(0)=10
• 6x=10
• x=10/6
• x=5/3, or 1 2/3
• The x intercept occurs at the point (5/3, 0)
• y intercept is where x=0
• 6(0)+2y=10
• 2y=10
• y=5
• The y intercept occurs at the point (0,5)
• If you draw those two points, (5/3,0) and (0,5), you can connect them to form the line given by the original equation.  Your point (3,-4) should land right on that line.