How do you figure out this math problem?

Question

What is the equation of the line that contains the points with (x,y) coordinates (–3,7) and (5,–1) ?

but HOW do you figure it out

Answer 1

The answer is y = -x + 4.

I've been out of college for a few years so this may be the long way of doing it but here goes ...

1. Given 2 points on the line, you find the slope.
2. Using the slope and 1 of the given points, find the y-intercept.
3. Plug everything you can into the equation y = mx + c (m = slope, c = y-intercept).

This is how you would actually carry out the above steps ...
1. Using the equation (X2 - X1) / (Y2 - Y1) you plug in numbers from your given points. You get the slope to be (5 - -3) / (-1 -7) = -1.
2. Using -1 and any of the given points, lets use (5, -1), you plug into y = mx + c to find the value of c. In this case you get -1 = -1(5) + c ... and after simplifying you get c = 4.
3. Now you take the same equation (y = mx + c) and plug in only the slope and y-intercept to come up with the general equation. In this case you get y = -1x + 4 which can be simplified to y = -x + 4.

Answer 2

In order to find the equation of a line passing through two points, you can use the point-slope form of the line, which is:

y-y₀ = m(x-x₀)

where (x₀, y₀) is one of the points on the line, and m is the slope of the line. To find the slope, simply divide the difference of the y-coordinates of any two points on the line by the difference of the x-coordinates of those same points. In this case, we have:

m=(7-(-1))/(-3-5) = 8/(-8) = -1

So now writing the equation of the line in point-slope form:

y-7 = -(x-(-3))

We can change this equation to slope-intercept form:

y-7=-(x+3)
y-7=-x-3
y=-x+4

And we are done.

Edit: corrected small error near the end.

Answer 3

draw in on a graph.alternatively, y=mx + c..
wre m is the gradient and c is the midpoint..

Answer 4

y=3x-2