How do you write an equation for 2 lines?

Question

You are given the points (1,2) and (0,3) for line a, and (6,1) and (2,-1) for line b.

Write the equation for lines a and b.

I have no idea what to do here.

Answer 1

Use the slope-intercept form for a line: y = mx + b where m is slope and b is the y intercept.

Slope equation is (y2 - y1)/(x2 - x1)

So for the first one, slope is (3 - 2)/(0 - 1) = -1

And the second one, slope is (1 - -1)/(6 - 2) = 1/2

You already know that the y-intercept for the first one is 3 because the point (0, 3) is given, so this equation is:

y = -x + 3

For the second one, you know that every time y goes down 1, x goes down 2 because the slope is 1/2.  So use (2, -1): If x goes down 2 to 0, y goes down 1 to -2, meaning the y-intercept here is -2.  This equation is:

y = x/2 - 2

And you can check by substituting the original points back into these equations.  But I don't feel like doing that.

Answer 2

for a ->

(y-2)/(3-2)=(3-2)/(0-1). (x-1)/(0-1)

for b ->

(y-1)/(-1-1)=(-1-1)/(2-6). (x-6)/(2-6)

Answer 3

To find the equation of a line, first find the slope of the line.

slope m = (y_2 - y_1) / (x_2 - x_1)

The slope for line a = (3 - 2) / (0 - 1) = 1/-1 = -1.

It is easier to find the equation of a line using slope-intercept form, which is y = mx + b.

So, so far we know that for line a, m = -1.  So, the equation for line a is y = -x + b.

Now, we use the points given for line a.  Choose either of the two points given to plug into the equation to solve for b (the y-intercept).  Let's use the point (0, 3):

y = -x + b

3 = 0 + b

3 = b

The equation for line a is y = -x + 3.

Use this same process to find the equation for line b:

m = (-1 - 1) / (2 - 6) = -2/-4 = 1/2

y = (1/2)x + b

1 = (1/2)(6) + b. I used the point (6, 1).

1 = 3 + b

-2 = b

The equation for line b is y = (1/2)x - 2.