Confused with y=mx+b?

Question

Find the equation of the line that passes through the points (-1,2) and (7,-2).

This is what it says in the book

Midpoint=
=(-2-2) / (7+1)
=-4 / 8
=-1 / 2

The answer is 7+2=-1/2(x-7) or y=(-1/2)x+(3/2)

So i guess i need to express it in y=mx+b
I got lost after finding midpoint -1/2. After that, where did 7+2, (x-7), and (3/2) come from? How do i find them?

Answer 1

Methinks your book has some typos.

The m in y = mx + b is the slope of the line, and b is the y-intercept.

The slope m of the line through two points (x1, y1) and (x2, y2) is given by the formula

m = ( change in y )/( change in x )= (y2 - y1)/(x2 - x1).

Using (x1, y1) = (-1, 2) and (x2, y2) = (7, -2) this becomes

m = (-2 - 2)/(7 - (-1)) = -4/(7 + 1) = -4/8 = -1/2.

The point-slope form of a line through the point (x0, y0) with slope m is

y - y0 = m(x - x0)

or

y = m(x - x0) + y0

Plugging in m = -1/2 and (x0, y0) = (7, -2) we have

y - y0 = m(x - x0)
y - (-2) = (-1/2)(x - 7)

distributing the multiplication by -1/2 and then adding (-2) to both sides gives

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

Another way to do it is to use one of the points you know the line goes through to find b, once you know what m is:

m = -1/2
y = mx + b
y = (-1/2)x + b
2 = (-1/2)(-1) + b ( since (x, y) = (-1, 2) is one point on the line)
3/2 = b.

Note that the point-slope form of a line y = m(x - x0) + y0 gives the slope-intercept form y = mx + b in the special case (x0, y0) is the y-intercept point (0, b).

The midpoint of (or the point halfway between) the two points (x1, y1) and (x2, y2) is the point

( [x1 + x2]/2, [y1 + y2]/2 )

so the m in y = mx + b doesn't stand for midpoint. It stands for slope (why I don't know; tradition I guess. It probably made sense at some point... :)

Answer 2

3x-2y=14 x=5+y Sorry -- I am a math teacher and you don't have to get this into y = mx + b. The second equation states that x is the exact same thing as 5 + y. Therefore, in the first equation, wherever there is an x, I can throw it out and put in 5 + y instead. 3(5 + y)-2y=14 15 + 3y - 2y = 14 15 + y = 14 y = -1 Now wherever you see a y in either of the equations, you can throw it out and put in -1. I am going to choose the second equation since it is easier. x=5+(-1) x = 4 So you now have a solution for x and a solution for y. Put your answer in coordinate form. (4, -1)

Answer 3

The midpoint formula that you used gives you the slope m. You still need to find out the intercept b. You can plug in either point (-1,2) or (7,-2) and solve:

y=mx+b
y=-(1/2)x+b
2=-(1/2)-1+b
b=3/2

Answer 4

(y2 - y1) / (x2 - x1) gives the slope of the equation y = mx + b and slope is m.

In the present case, the slope is (-2 - 2) / (7 + 1) = -4/8 = -1/2

So, y = -1/2 x + b

Substituting the value of x1 and y1, we get

2 = -1/2 x -1 + b

= 1/2 + b

So, b = 2 - 1/2 = 3/2

So, the equation is y = -1/2x + 3/2

Answer 5

You can solve the equation by point-slope form
i.e.,y-y1=m(x-x1) where m=(y2-y1)/(x2-x1),you no need to calculate the midpoint and do the problem.

Answer 6

find slope first
m=deltay/delta x
m=4/-8=-1/2
y=-x/2 +b
solve for b by substitution
2=(1)/(2)+b
b=3/2
y=-x/2+3/2
2y+x=3
y=

Answer 7

y – y1 = m(x – x1)

Answer 8

oh no... bad memories of economics...