Help with slope equations.. please?

Question

I need an equation (in slope-intersept form) for each pair of coordinates.

(0,-2) (2,0) and (1,-1) (0,1)

Answer 1

Between points (x1, y1) and (x2,y2), the slope is m=(y2-y1)/(x2-x1). Then the y-intercept is b=y1-m*x1. This assumes that x1 <> x2.

If x1=x2, the line between the points is parallel to the y axis and therefor has an undefined slope and no y-intercept. The equation is x=x1.

Answer 2

Firstly, we need to get to a formula where y=mx+b where m is the slope and b is the y-intercept.

So, the slope is defined as the change in y divided by the change in x. In the first set of points, that means:

0-(-2)/2-0 = 2/2 = 1

Now, you happen to be given the y-intercept. That's because the point (0,-2) lies on the y-axis. So the y-intercept is -2.

The form of the equation is: y=x-2

As for the second set of points:

1-(-1)/0-1 = 2/-1 = -2

Again, you have the y-intercept since the point (0,1) sits on the y-axis. The y-intercept is 1

So, the equation of the line is y = -2x+1

Answer 3

Slope-intercept form :

y = mx + b

m = slope ; b = y-intercept

Step 1 : Solve first : m = (y2 - y1) / (x2 - x1)

Step 2 : Using the coordinates of any point on the given pair , substitute the x & y coordinates of the selected point to the equation y = mx + b , and solve for b :

Example : Using points (0, -2) & (2, 0)

m = [ 0 - (-2)] / (2 - 0) = 2/2 = 1

Using point (2, 0) --> x = 2 ; y = 0

y = mx + b
0 = 1(2) + b
-2 = b

so the general equation : y = x - 2

Answer 4

Unfortunately, I don't think answering your homework for you is the right way to go about it. However, I can help you out w/ examples so that you can work on future problems:

First your two coordinates are in (x,y) form.

The equation to solve for slope intercept is as follows:

(y2-y1) = m * (x2-x1)

m is what you are solving for (slope).

if you had coordinates (1,2) and (3,4) the equation would be:

(4-2) = m * (3-1)

because:

y2 = 4
y1 = 2
x2 = 3
x1 = 1

(you can switch which number is y2 and y1 as long as the x2 is still from the same coordinate as y2 and x1 is from same coordinate as y1)

To Solve:

(4-2) = m * (3-1)

2 = m * (2)

2/2 = m * (2)/2

1 = m

Answer 5

Pick one coordinate from each set as your main coordinate. y-y1 = (y2-y1)/((x2-x1)*(x -x1)

for the first one
y- -2 = (0- -2)/(2-0)*(x - 0)
y+2 = -x

for the second one
y-1 = (-1-1)/(1-0)* (x-0)
y-1 = -2x

Answer 6

If you are given two points, use this formula:
(y-y1)/(x-x1) = (y2-y1)/(x2-x1).

So (y-(-2))/(x-0) = (0-(-2))/(2-0)
(y+2)/x = 2/2 =1
y+2= x
y = x-2

You should be able to now work the secon one yourself.