Question

Find the equation of the line between the points (8,-4),(7-6)

Answer 1

I didn't know what form you wanted the line in.

Slope-intercept form: y=2x-20

Standard form: 2x-y=20

Point-slope form: y+4=2(x-8) or y+6=2(x-7)

You gave the points (8,-4) and (7,-6).

That last point was (7,-6) right? I seen (7-6) and just thought you probably meant (7,-6.

Explanation:

Equation of a line in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

To find the slope: I'm going to line up the points vertically and subtract them vertically, then put 2nd difference over 1st difference.

I feel like some people like this more than the formula
`(y_2-y_1)/(x_2-x_1)` or
`(y_1-y_2)/(x_1-x_2)`. It is the same thing just a different way to organize things.

So let's do the finding of the slope:

( 8 , -4)

-( 7 , -6)

-------------

1 2

So the slope is 2/1=2.

So we have m=2.

Let's input into our equation y=2x+b.

We need to find the y-intercept. We could do that by using a point on the line. We get to choose between (8,-4) or (7,-6). It does not matter.

y=2x+b with (8,-4)

-4=2(8)+b

-4=16+b

Subtract 16 on both sides:

-4-16=b

-20=b

So the y-intercept is -20.

The equation is y=2x+-20 or y=2x-20 (your pick-same thing).

Now let's also put it in standard form which is ax+by=c where it is preferable to have a,b, and c as integers. (Integers are {...,-3,-2,-1,0,1,2,3,...}.)

y=2x-20

Subtract 2x on both sides:

-2x+y=-20

This is in ax+by=c form.

You could multiply both sides by -1:

2x-y=20.

This is still in standard form.

Let's also go for point-slope form which is y-y1=m(x-x1) where (x1,y1) is a given point on the line and m is the slope.

We already have the slope is 2.

We have two points to choose from. Choose one and go with it. Let's choose (x1,y1)=(8,-4).

y-(-4)=2(x-8)

or

y+4=2(x-8)

Now if you did go with the other point (x1,y1)=(7,-6) it would be:

y-(-6)=2(x-7)

y+6=2(x-7)

You are probably wondering how those are the same lines. Let's confirm. Solve both of them for y.

y+4=2(x-8)

Distribute 2:

y+4=2x-16

Subtract 4 on both sides:

y=2x-16-4

Simplify:

y=2x-20

Now the other line:

y+6=2(x-7)

Distribute 2:

y+6=2x-14

Subtract 6 on both sides:

y=2x-14-6

y=2x-20

Answer 2

y=-2x+20 or y-4=-2(x-8)

Explanation:

first we need to calculate the slope

y2-y1/x2-x1

-6+4/7-8

-2/1

The slope is -2

Nows lets find the y intercept using

y-y1=m(x-x1)

y-4=-2(x-8)

y-4=-2x+16

+4 +4

y=-2x+20

Y intercept is 20