Finding points on a line: (2, A3) is on line with (0, A1) and(1, A2)

a6m3

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May 15, 2017
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Hi, Im having trouble with the problem,

The point (2, A3) lies on the line through the points (0, A1) and(1, A2). Find A3

I have no idea where to start or what to do

Someone please help me :(

Thanks in advance
 

mmm4444bot

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Oct 6, 2005
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The point (2, A3) lies on the line through the points (0, A1) and (1, A2).

Find A3

I have no idea where to start or what to do.
You can express the value of A3 in terms of A1 and A2.

Use the Slope Formula with the coordinates of the two given points (0, A1) and (1, A2) to calculate an expression for the slope of the line.

Then use the Point-Slope Form to write an equation for the line -- use the slope expression and the known point (0, A1).

Finally, substitute into the equation of the line the x- and y-coordinates from the third given point, and solve for A3.

Please show your work, if you get stuck. :cool:
 

a6m3

New member
Joined
May 15, 2017
Messages
2
You can express the value of A3 in terms of A1 and A2.

Use the Slope Formula with the coordinates of the two given points (0, A1) and (1, A2) to calculate an expression for the slope of the line.

Then use the Point-Slope Form to write an equation for the line -- use the slope expression and the known point (0, A1).

Finally, substitute into the equation of the line the x- and y-coordinates from the third given point, and solve for A3.

Please show your work, if you get stuck. :cool:

Got it, Thank You for the reply :p
 

HallsofIvy

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Jan 27, 2012
Messages
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Equivalently: any non-vertical line can be written y= ax+ b. Set x= 1 and y= A1 in that equation to get one equation for a and b. Set x= 2 and y= A2 to get a second equation for a and b. Solve the equations for a and b (they are particularly easy equations). Finally, set x= 2 in that equation and calculate A3.
 
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