SOLUTION: A line goes through the coordinate (3,4) and through (5,1). Find a line of the form y=ax+b.

Question 112937This question is from textbook
: A line goes through the coordinate (3,4) and through (5,1). Find a line of the form y=ax+b. This question is from textbook

Found 2 solutions by jim_thompson5910, chitra:
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

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 (note: if you need help with combining fractions, check out this solver)

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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 chitra(359) (Show Source): You can put this solution on YOUR website!
The line equation passing through two points in the slope intercept form is given by:

which is nothing but y = ax + b

Where m = (3, 4) and (5, 1)

m =

==> m =

Substituting in the line equation we get:

(y - 4) = (x - 3)

==> 2y - 8 = -3x + 9

==> 2y = -3x + 9 + 8

==> 2y = - 3x + 17

==> y =

thus the line equation

Hence, the solution

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