(Solved) How to find the intercept of two lines?

micooo

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11 years ago

I need to find the intercept for
y=1/4x + 3
y=3/4x + 4

I tried graphing the equations but they intercept in-between intervals and it's difficult to get the accurate intercept when graphing by hand. Is there any other way?

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micro205

wrote...

11 years ago

Set your equations equal to each other:
3/4x + 4 = 1/4x + 3

Solve it:
3/4x - 1/4x = 3 - 4
1/2x = -1
x = -2

Substitute in 1 of your equations:
y = 1/4 (-2) + 3
y = 2 1/2

So your intercept is at x=-2 and y=2 1/2.

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smokebomb13

wrote...

11 years ago

y = (1/4)*x + 3
y = (3/4)*x + 4

Where the lines intercept, the value of y will be the same. Just equate

(1/4)*x + 3 = (3/4)*x + 4

x + 12 = 3*x + 16

-2*x = 4

x = -2 <<<

y = (1/4)*x + 3 = -(1/2) + 3 = 5/2 <<<

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ilohim

wrote...

11 years ago

So you know that at the intersection (we'll call that point a,b) that both a and b satisfy the equations y = 1/(4x) + 3 and y = 3/(4x) + 4

so now you know, b = 1/4a + 3 and b = 3/4a + 4
since both equations equal to b on one side, we can let the other sides equal to each other

b = 1/4a + 3 = 3/4a + 4

so 1/4a + 3 = 3/4a + 4
solve that and you get a = -1/2

now you sub (-1/2, b) back into either equations and you get b = 7/2

hope my solution was lucid and understandable! Grinning Face

and happy christmas eve!

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smmunday

wrote...

11 years ago

y=1/4x + 3
y=3/4x +4
1/4x + 3 = 3/4x + 4
x + 12 = 3x + 16
-2x + 12 = 16
-2x = 4
x = -2
y = (1/4)(-2) + 3
y = 2.5

intercept = (-2,2.5)

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