Linear Equation Help?

Question

Find in standard from, Ax + By = C, the equation of the line such that the sum of the x and y intercepts are 3 and the line passes through (-1,4)

Answer 1

There are 2 such lines. One has x-int of 1 and y-int of 2, and one has x-int of -3 and y-int of 6. Here is why:

If the x-intercept point is (x,0) then the y-intercept would
be (0, 3-x) and a third point is goven to be (-1,4)

The slope of the line is either (3 - x - 4)/(0 - -1) or
(0 - 4)/(x - -1), and these must be equal.

So (3-x-4)(x - -1) = (0-4)(0 - -1)

(-1 - x)(x+1) = -4(1)

-x^2 - 2x - 1 = -4

0 = x^2 + 2x - 3

0 = (x+3)(x-1)

The equation of the line through (1,2) and (-1,4) is found by getting its slope : (4-2)/(-1-1) = -2 and using point-slope

y - 2 = -2(x - 1)

y - 2 = -2x + 2

y + 2x = 4

You can do the other one

Answer 2

x+y=3

Answer 3

First find the slope of the line. You need two points to do it, and you have three. Choose from (3,0), (0,3), and (-1,4). The formula for slope is x-sub-2 minus x-sub-1 *OVER* y-sub-2 minus y-sub-1. Then set it up in a different equation. I can't remember what this form is called, but one of the equations for a line is y-sub-2 minus y-sub-1 *EQUALS* m(x-sub-2 minus x-sub-1) Simplify it until you get it into slope intercept form: y=mx+b Finally, subtract mx from both sides and it will be in standard form, unless m is a fraction, in which case you need to multiply both sides of the equation by the denominator of that fraction. By the way, x-sub-2=The x coordinate of one point, while x-sub-1=The x coordinate of a different point. The same goes with y-sub-2 and y-sub-1. m=slope. b *LOWERCASE b* = y intercept

Answer 4

im in 8th grade in enriched algebra
we did something like that but used different letters for the formula
i dont fully understand your question but
-1 would be x and 4 would be y
if you have to plot this you would go over -1 and up 4 and that would be were the point would be
to remember which you do first you can use this saying
YOU MUST MOVE OVER (LEFT OR RIGHT)(X-axis)THE LADDER BEFORE YOU CAN GO UP (DOWN) (Y-axis)THE LADDER

Answer 5

Well, i'm in 8th grade and we did Linear equations last week. I am also in algebra 1 class. And yet, we haven't done a problem like that.. Sorry.

Answer 6

-1 < that being x
4 < that being y = -1+4=3
is that suppose to be a trick question?

Answer 7

-a+4b=c
x int
ax=c
x=c/a
y int
by=c
y=c/b

c/a+c/b=3
bc+ac=3ab
-a+4b=c

2 equations & 3 unknowns. I don't think a unique solution exists.