SOLUTION: I really need help on this problem: If f is a linear function and f(0)= 10 and f(10)= 14, find f(5) and f(-5). PLEASE HELP ME!!!!!!!!

Question 87678: I really need help on this problem: If f is a linear function and f(0)= 10 and
f(10)= 14, find f(5) and f(-5).
PLEASE HELP ME!!!!!!!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If this means we have a point (0,10). If this means we have a point (10,14). So we can find the equation of the line through the two points

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.

So now we have the equation

which means

Lets now find

Plug in

Multiply

Reduce

Add

So

Lets now find

Plug in

Multiply

Reduce

Add

So

Notice if we graph we get:

graph of which goes through the points (0,10),(10,14),(5,12),(-5,8)

Notice how the line goes through all of the points. This verifies our answer.
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