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

[a6m3]

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]

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]

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

 

[HallsofIvy]

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.