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

In summary, to find the x-coordinates of points A and B, we can solve for x in the given equation and plug in the given y-values. This gives us x-values of 1 for point A and 3 for point B.
  • #1
mathdad
1,283
1
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?
 
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  • #2
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
 
  • #3
Not too bad.
 
  • #4
What do you get when you solve for x?
 
  • #5
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)
 
  • #6
\(\displaystyle x(y)=2(y-1)\)

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

\(\displaystyle x_B=x\left(y_B\right)=2(2.5-1)=3\)
 
  • #7
By solving the given equation for x, it is faster.
 

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

What are coordinates?

Coordinates are a set of numbers that describe the position of a point in space. They are used to locate points on a map or graph.

How are coordinates written?

Coordinates are written as an ordered pair (x, y) where the first number represents the horizontal position and the second number represents the vertical position. The two numbers are separated by a comma.

What is the difference between the x-coordinate and y-coordinate?

The x-coordinate represents the horizontal position of a point, while the y-coordinate represents the vertical position. Together, they pinpoint the exact location of a point in space.

How do you find the coordinates of a point on a graph?

To find the coordinates of a point on a graph, locate the point on the x-axis and y-axis. The x-coordinate is the number that corresponds to the point's position on the x-axis, and the y-coordinate is the number that corresponds to its position on the y-axis.

What are the different types of coordinates?

There are three main types of coordinates: cartesian coordinates, polar coordinates, and geographic coordinates. Cartesian coordinates use x and y axes to locate points in a two-dimensional plane. Polar coordinates use a distance and angle to locate points in a two-dimensional plane. Geographic coordinates use latitude and longitude to locate points on the Earth's surface.

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