Intercepting Lines: find where Y=-3/4X-2, Y=5/2X+9 meet

[James98765]

If you have the slope-intercept equation of two different lines how do you calculate where the meet? For instance:

1.) Y = -3/4X - 2
2.) Y = 5/2X + 9

This question doesn't seem very hard to me I just can't picture how to put it together in my head. If anyone could show me how this works that would be great. Thanks!

 

[Deleted member 4993]

Re: Intercepting Lines

If you have the slope-intercept equation of two different lines how do you calculate where the meet? For instance:
1.) Y = -3/4X - 2
2.) Y = 5/2X + 9
This question doesn't seem very hard to me I just can't picture how to put it together in my head. If anyone could show me how this works that would be great. Thanks!

At the point of intersection, the (x,y) of the point will belong to both the lines.

So equate the 'y' s and solve for 'x':

-(3/4)*x - 2 = (5/2) *x + 9

then use the resulting 'x' in any of the equations to find 'y'.

If you are still stuck - write back showing your work.

 

[Mrspi]

Re: Intercepting Lines

If you have the slope-intercept equation of two different lines how do you calculate where the meet? For instance:
1.) Y = -3/4X - 2
2.) Y = 5/2X + 9
This question doesn't seem very hard to me I just can't picture how to put it together in my head. If anyone could show me how this works that would be great. Thanks!

You are given two equations:

y = (-3/4)x - 2
y = (5/2)x + 9

You could graph the two lines, and see if you can determine the coordinates of the point where they intersect. However, it is sometimes difficult to "see" the intersection point.

It's MUCH easier to find the solution algebraically.

Do you see that you are given two expressions, each equal to y? If each expression is equal to y, then the two expressions must be equal to each other. So,

y = y
(-3/4)x - 2 = (5/2)x + 9

Now...solve that for the value of x. That will give you the x-coordinate of the point where the two lines intersect. To find the y value, pick either of the equations
y = (-3/4)x - 2 or
y = (5/2)x + 9

Substitute the value you've found for x, and see what y is. As a very good check...substitute your value for x into BOTH of these equations. Do you get the same value for y? YOU SHOULD.

 

[James98765]

Thanks alot guys. I can see how it works now!