# Quick question on math?

Write a linear system that has a point of intersection of (2,-4).

(1)

(2)

### 8 Answers

- PuzzlingLv 72 months agoFavourite answer
Start with slope-intercept form:

y = mx + b

Pick an arbitrary value of m:

m = 1

y = x + b

Plug in x=2, y=-4

-4 = 2 + b

b = -4 - 2

b = -6

There's your first equation:

y = x - 6

Now pick a different arbitrary slope:

m = 2

y = 2x + b

Plug in the point again:

-4 = 2(2) + b

-4 = 4 + b

b = -4 - 4

b = -8

There's your second equation:

y = 2x - 8

You could pick any 2 different values of m and make this work.

Answer (one of infinitely many possibilities):

[1] y = x - 6

[2] y = 2x - 8

Source(s): https://www.desmos.com/calculator/mbnskvywh5 - ?Lv 62 months ago
You can have any slope you want. So pick the slope, and solve for the y-intercept that puts (2, -4) on the line.

1) Let slope be, say, 6

y = 6x + b

-4 = 6(2) + b

b = -16

y = 6x - 16 is one line.

2) Let slope be -3

y = -3x + b

-4 = -3(2) + b

b = 2

y = -3x + 2 is another line.

- Anonymous2 months ago
The equation of any straight line through the point (X.Y) is;

y- Y = m(x-X)

where m is the gradient.

X=2 and Y=-4 and you can pick *any* 2 values of m. E.g.

m=1 gives y-(-4) = 1(x-2 )

y = x - 6

m=2 gives y-(-4) = 2(x-2 )

y = 2x - 8

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- ?Lv 72 months ago
The equation of a line y₁ passing through (2,-4) with slope 4 is

y₁ - -4 = 4(x - 2)

y₁ = 4x - 12

The equation of a line y₂ passing through (2, -4) with slope -¾ is

y₂ - -4 = -¾(x - 2) y₂ = -¾x - ⁵⁄₂

A system of linear equatinons that has a point of intersection of (-2,4) is

(1) y₁ = 4x - 12 .....................ANS

(2) y₂ = -¾x - ⁵⁄₂ .ANS

- llafferLv 72 months ago
You can set up two general linear equations based on this form:

y = mx + b

Where x = 2 and y = -4 in both with different slopes (m). I'll use m = -1 and m = 2. That gives us:

-4 = -1(2) + b and -4 = 2(2) + b

-4 = -2 + b and -4 = 4 + b

-2 = b and -8 = b

Now that we have two b's complete the equations:

y = -x - 2 and y = 2x - 8

That is one of many systems of equations that will have the point (2, -4) as a solution.