SOLUTION: Given a line containing the points (1,4),(2,7),and(3,10) determine the slope-intercept form of the equation, provide one additional point on this line, and graph the function.

Question 87297: Given a line containing the points (1,4),(2,7),and(3,10) determine the slope-intercept form of the equation, provide one additional point on this line, and graph the function.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Lets find the equation of the line through the two points (1,4) and (3,10)

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

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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)

Distribute

Multiply and to get . Now reduce to get

Add to 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.

Now lets plot the point (2,7) and

graph of with the point (2,7)

Since the point is on the line, the equation of the line that goes through (1,4),(2,7),and(3,10) is

Now lets pick any other x value so we can plot another point. Let x=0

plug in

So we have another point (0,1)

So we have this graph and these points

graph of with the points (0,1),(1,4),(2,7), and (3,10)

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