MHB How Do You Find the X-Coordinates of Points A and B on the Line y = (x/2) + 1?

[mathdad]

The equation y = (x/2) + 1 is given. It forms a straight line going through the points A(x, 1.5) and B(x, 2.5). Find the x-coordinates of points A and B.

Do I substitute the value of y for each point into the given equation and solve for x individually?

 

[MarkFL]

Since we are given y's and asked for the corresponding x's, I would write the given linear equation as a function of y (solve for x), and then plug in the y's to get the corresponding x's. :D

 

[mathdad]

Not too bad.

 

[MarkFL]

What do you get when you solve for x?

 

[mathdad]

For A(x, 1.5) we have

1.5 = (x/2) + 1

1.5 - 1 = x/2

0.5 = x/2

0.5(2) = x

1 = x

A(1, 1.5)

For B(x, 2.5) we have

2.5 = (x/2) + 1

2.5 - 1 = x/2

1.5 = x/2

1.5(2) = x

3 = x

B(3, 2.5)

 

[MarkFL]

$$x(y)=2(y-1)$$

$$x_A=x\left(y_A\right)=2(1.5-1)=1$$

$$x_B=x\left(y_B\right)=2(2.5-1)=3$$

 

[mathdad]

By solving the given equation for x, it is faster.