What is the equation of a line that passes through the points (-2,2) and (1,0) in y=mx+b form?

Question

Solve for b

Answer 1

Pick (1,0) and use point-slope form,
y-0 = m(x-1)
y -0 = [(0-2)/(1+2)](x-1)
y = -(2/3)x+2/3

Answer 2

To do this, you first have to recognize that the slope (m) is defined as change in y/ change in x

so, 0-2/1-(-2) = -2/3

Now, you need the y-intercept (b). To get that, you assume that the line travels through a point (0,y) and one of the other points. Since the slope must be the same as through the first two original points, you can solve for y. Let's use the point (1,0) for this purpose.

So, 0-y/1-0 = -y = -2/3 or y=2/3

So the equation of the line is y=-2/3x + 2/3

Answer 3

First find the slope m

m = (y2 - y1) / (x2 - x1)
m = (2 - 0) / (-2 - 1)
m = 2 / -3
m = -2/3

So we have y = -2x/3 + b

So pick one of the points and plug in x and y to find b.

0 = (-2 * 1)/3 + b
0 = -2/3 + b
b = 2/3

y = -2x/3 + 2/3

Try it on the other point to check

2 = (-2 *-2)/3 + 2/3
2 = 4/3 + 2/3
2 = 2

QED

Answer 4

m = slope = diff. in y's/diff. in x's = (2 - 0)/(-2 - 1) = 2/-3
Now we have, y = -2/3x + b
You can plug in either set of points to find the y-intercept(b).
Using the first set:
2 = -2/3(-2) + b
2 = 4/3 + b
2 - 4/3 = 4/3 + b - 4/3
*NOTE 2 = 6/3
2/3 = b

If you used the other point, it is much simpler:
0 = -2/3(1) + b
0 + 2/3 = -2/3 + b + 2/3
2/3 = b

The eqaution of the line is y = -2/3x + 2/3

Answer 5

substitute the values of given coordinates to the equation
for (-2,2) i.e. 2= -2m + b
for (1,0) i.e. 0= 1m + b
sub both eqs:
finally 2=-3m
m = -2/3
substitute value of m in 0=1m+b to get value of b=2/3
therefore the equation is
y=-2/3x + 2/3
or 3y=-2x+2

Answer 6

just substitute the values of x&y to the equation
for (-2,2), 2= -2m + b
for (1,0), 0= 1m + b
then equate the values of b:
-m = 2 + 2m
m = -2/3
therefore the equation is
y=-2/3m + b

Answer 7

The equation of the straight line through (x1, y1) and (x2, y2), if x1 ≠ x2, is:

y - y1 = [ (y1 - y2) / (x1 - x2) ] (x - x1)
y - 2 = [ 2 - 0) / (-2) - 1 ] [(x - (-2)]
y - 2 = [ (2) / (-3) ] (x+2)
y - 2 = -(2/3) (x+2)
y = (-2/3)x - (4/3) + 2
y = (-2/3)x - (4/3) + (6/3)
y = (-2/3)x - (2/3)

Answer 8

didn't you ask the same type of question minutes ago?

y2-y1 over x2-x1 and you'll find slope. take any x/y and plug into y=mx+b and you'll get your answer.