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Question 226744: find an equaion of the line containing the given pair of points.
(2,3) and 6,4)
What is the equation of the line?
y = ?
Answer by drj(1380)   (Show Source):
You can put this solution on YOUR website! Find an equaion of the line containing the given pair of points.
(2,3) and (6,4)
What is the equation of the line?
y = ?
Step 1. We will put the equation of the line in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).
Step 2. The slope of the line m is given as
where for our example is x1=2, y1=3, x2=6 and y2=4 (think of  ). You can choose the points the other way around but be consistent with the x and y coordinates. You will get the same result.
Step 3. Substituting the above values in the slope equation gives
Step 4. The slope is calculated as  or
Step 5. Now use the slope equation of Step 2 and choose one of the given points. I'll choose point (2,3). Letting y=y2 and x=x2 and substituting in the slope equation given as,
Step 6. Multiply both sides of equation by x-2 to get rid of denomination found on the right side of the equation
Step 7. Now simplify and put the above equation into slope-intercept form.
Add 3 from both sides of the equation
 This is in slope-intercept form where the slope m=1/4 and y-intercept b=0
Step 8. See if the other point (6,4) or x=6 and y=4 satisfies this equation
 So the point (6,4) satisfies the equation and is on the line. In other words, you can use the other point to check your work.
Step 9. ANSWER: The equation of the line is
Note: above equation can be also be transform into standard form as
See graph below to check the above steps.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
Good luck in your studies!
Respectfully,
Dr J
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