Containing the points (0,2) and (2,0)?

Question

Determine hte equation for each line, using the information given

Answer 1

Find the slope: 2-0 / 0-2 = -1 and the y-intercept is (0,2) so the equation is y = -x+2

Answer 2

Graph the two intercepts given and draw a line. This is a single line. You are looking for the equation for this line. You may have seen the following equation in class:

y = mx + b

This is the general slope-intercept form of the equation of a line. It is called the slope-intercept form because the letter m is the slope and b is the y-intercept.

By studying the picture I asked you to draw, you should immediately see the y-intercept, b, is 2. Therefore, you are half-way home with the following:

y = mx + 2

Now, look at the picture and determine the slope. Slope can be determined by remembering

rise
―― = slope
run

Notice that in your picture you go down two units and then two units to the right. (There is a formula that can be used, but, at this stage of the learning process, it would be more beneficial if you would just use the picture to determine the slope.) So, your slope is

-2
― = -1 = slope = m
2

Substitute this into your half-finished equation and you are done.

y = -1x + 2

or

y = -x + 2

If the teacher wants the standard form of the equation of a line,

Ax + By = C,

then you will have to add x to both sides of your slope-intercept equation and obtain the desired equation.

x + y = 2.

Answer 3

One way to do this is to use the points and the slope-intercept form of the equation:

y = mx + b

At the point (0, 2)

2 = m(0) + b
2 = b

With this information and at point (2, 0)

0 = m(2) + 2
-2 = 2m
-1 = m

So we can write

y = -x + 2

Answer 4

Given two points the general equation of a line passing through them (in 2D) is

y - y1 = [y2 - y1] / [x2 - x1] * ( x - x1)

Where the two points are (x1,y1) and (x2,y2)

In your case let (x1,y1) = (0,2) and (x2,y2) = (2,0) (doesnt matter which is which will give the same answer)

y - 2 = [0 - 2]/[2-0] * (x - 0)

y = -x + 2

or

y = 2 - x

You can easily verify that that contains the two points.

Answer 5

They both managed to break even, I think we can call it a day.