SOLUTION: which an equation of the line that passes though the point (5,2) and (10,-3)

Question 1194391: which an equation of the line that passes though the point (5,2) and (10,-3)

Found 3 solutions by josgarithmetic, math_tutor2020, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
typical, common,
look for other already solved examples.
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Let's find the slope first.
(x1,y1) = (5,2) and (x2,y2) = (10,-3)
m = slope
m = rise/run
m = (change in y)/(change in x)
m = (y2 - y1)/(x2 - x1)
m = (-3 - 2)/(10 - 5)
m = (-5)/(5)
m = -1
The slope is -1

Now let's find the y intercept
I'll use the slope we just found and the first point (x1,y1) mentioned.
Use point-slope form
y-y1 = m(x-x1)
y-2 = -1(x-5)
y-2 = -1*x-1*(-5)
y-2 = -x+5
y = -x+5+2
y = -x+7

This equation is in y = mx+b form
m = -1 = slope
b = 7 = y intercept

Answer: y = -x+7
To verify this answer, plug in each coordinate into the equation. Then simplify. You should get the same thing on both sides.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
which an equation of the line that passes though the point (5,2) and (10,-3).
~~~~~~~~~~~~~~~~

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To help you to develop such skills, special lesson was created in this site
    - Equation for a straight line in a coordinate plane passing through two given points

Read it and then solve your problem.

From this lesson, learn the subject once and for all.

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