SOLUTION: (writing linear equations in point slope form) write the point-slope form of an wquation of the line that passes through each pair of points. (-1,-7),(1,3)

Question 118262: (writing linear equations in point slope form)
write the point-slope form of an wquation of the line that passes through each pair of points.
(-1,-7),(1,3)
Found 2 solutions by jim_thompson5910, TP:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First lets find the slope through the points (,) and (,)

Start with the slope formula (note: is the first point (,) and is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

Reduce

So the slope is

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Now let's use the point-slope formula to find the equation of the line:

------Point-Slope Formula------
where is the slope, and is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Rewrite as

Rewrite as

Distribute

Multiply and to get

Subtract from both sides to isolate y

Combine like terms and to get
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Answer:

So the equation of the line which goes through the points (,) and (,) is:

The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is

Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver )

Graph of through the points (,) and (,)

Notice how the two points lie on the line. This graphically verifies our answer.
Answer by TP(29) (Show Source): You can put this solution on YOUR website!
m(the gradient)=vertical distance between the two points/horizontal distance between the two points.
So m=(Y-y)/(X-x) where the two points have coordinates of (X,Y) and (x,y).
So here (X,Y)=(-1,-7) and (x,y)=(1,3).
Hence the gradient m=(-7-3)/(-1-1)=-10/-2=5.
Now the general equation of a straight line is y=mx+c where m is the gradient and c is the y intercept(the y value where the line crosses the vertical Y axis).
So far we have: y=5x+c.(i)
We need to find the value of c.
Since the line passes through (1,3) then we can replace x and y in our equation by 1 and 3 respectively.
This gives (i) as: 3=5*1+c
So 3=5+c
Subtract 5 from each side of the equation and we get: 3-5=c
So c=-2
Hence the required equation is y=5x-2 ANS
(N.B. You should verify your answer by replacing the x by -1 and the y by -7)
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