SOLUTION: how would I graph the line with a slope of 3 and passes through points (2,1) and (4,7).

Question 115649: how would I graph the line with a slope of 3 and passes through points (2,1) and (4,7).
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If you only want to graph the line, simply plot the two points (2,1) and (4,7) and draw a straight line through them.

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However, if you want to find the equation of the line, then...

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

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.
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