SOLUTION: Could you please help me solve and understand this equation? Find an equation of the line containing the given pairs of points (4,3) and (12,7) Y=

Question 87561: Could you please help me solve and understand this equation?
Find an equation of the line containing the given pairs of points
(4,3) and (12,7) Y=
Found 2 solutions by ankor@dixie-net.com, jim_thompson5910:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Could you please help me solve and understand this equation?
Find an equation of the line containing the given pairs of points
(4,3) and (12,7) Y=
:
There are two formulas that you should know when dealing with slope equations:
:
1st one is the "slope equation": m =
:
Assign the given coordinates as follows:
x1=4, y1=3, x2=12, y2=7
:
Using the slope equation and these values, find the slope
m = = =
:
The 2nd formula you should know is the "point/slope equation": y-y1 = m(x-x1)
:
Using the values: m = 1/2 or m = .5; x1=4, y1=3
y - 3 = .5(x - 4)
y - 3 = .5x - 2; multiplied what was in brackets
y = .5x - 2 + 3; added 3 to both sides
y = .5x + 1; is the equation derived from the given coordinates
:
You can always check the equation by substituting the value for x and seeing if the gives you the given value for y:
Using x=4 and y = 3
y = .5(4) + 1
y = 2 + 1
y = 3
:
You can do the same with the 2nd set of coordinates.
Using x = 12, y = 7
y = .5(12) + 1
y = 6 + 1
y = 7
:
I tried to explain this step by step, let me know if it helped you understand it.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Finding the Equation of a Line

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

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

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)

Distribute

Multiply and to get . Now reduce to get

Add to both sides to isolate y

Combine like terms and to get

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

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.

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