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

#### a6m3

##### New member
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

#### mmm4444bot

##### Super Moderator
Staff member
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.

#### a6m3

##### New member
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.

Got it, Thank You for the reply

#### HallsofIvy

##### Elite Member
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.