59) find the equation of the line that passes through points (2,0) (-4,0) and (0,-4).?

Question

the answer is y= 1/2x^2 + x -4
how do i get there?

Answer 1

The question is incorrectly stated. The answer you gave is the equation of a parabola, not a line. And indeed a straight line cannot go thru all three points. The question should be: find the parabola that goes thru the three given points.

If the parabola is vertical we have a parabola of the form:
ax² + bx + c = y

We have three equations and three unknowns.

4a + 2b + c = 0
16a - 4b + c = 0
0a + 0b + c = -4

Solving we get:

a = 1/2
b = 1
c = -4

So the equation of the parabola is:

y = (1/2)x² + x - 4

Answer 2

this is a trick question. The line is undefined. You do not have enough information.

actually you have too much information. because your plot points do not lie in a line. They make a sort of V shape . Lines don't bend like that.

now if you were doing trig, with sine/cos or some other interesting math or even parabolas you could have a function that passes through those points, but no line does.

now if it said find the equation of the LINES that pass through these points, you could then come upw ith 6 new lines and equations pretty easily.

The person below me is WRONG. Not completely wrong. If you plug in your points it works for one data set (0,-4), but it does not work for the others. If you plug in the x in the (-4,0) set you get out a -12 for the Y value. Which is the WRONG answer. the set you are given is -4,0 not -4,-12 So the equation of the line she gives is WRONG.

This is a trick question as you have written it. and if you plot the points given, this is no longer a LINE. It looks lIke a V. now if you have to come up with the equations of the line segments that is very different from what you asked. You would then end up with 2 equations

Answer 3

If its a straight line then use two of the points in the point-gradient formula to get the answer.

The equation is

y - y1 = y2 - y1
x - x1__ x2 - x1

so using the points (2,0) and (0, -4)

y - 0 = -4 - 0
x - 2 __ 0 - 2

y ___= 4
x - 2 ___2

y = 2(x-2)

y = 2x -4

Answer 4

Let us find the slope(m0 of the line
m=y2-y1/x2-x1

consider any 2 points,say (2,o) (-4,0).
m=0-0/-4-2

so m=0

then equation of line
y-y1=m(x-x1)
y-0=0(x-2)
y=o

so the conclusion is that there is no straight line passing through the given lines but a curve.