x coordinate

Question

two points on a line are (4,-8) and (2,-5). If the y coordinate of another point on the line is -3, what is the x coordinate?

Answer 1

Use the first two points to find the slope of the line

 

[-5 - (-8)] divided by (2 - 4)

 

= (-5 + 8)/-2 

 

= -3/2 

 

Now, call the third coordinate (x , -3)

 

We know the slope = -3/2 

 

Now, let's choose the second point (2, -5) to find the value of x for the third coordinate

 

[-5 - (-3)]/(2 - x) = -3/2

 

(-5 + 3)/(2 - x) = -3/2

 

-2/(2 - x) = -3/2

 

-4 = -3(2 - x)

 

-4 = -6 + 3x

 

2 = 3x

 

2/3 = x

 

 

 

Answer 2

We start by finding the slope: 

 

(y2-y1)/(x2-x1) = (-5 - -8)/(2-4) = 3/-2 = -3/2.

 

The slope tells you that each time you move right 2 spaces in the X, you'll move down 3 spaces in the Y.

 

Pick a Y coordinate.  Either one will do.  Let's take -5.  To get from there to -3, we need to move UP 2 spaces.  To find out how many we need to move in the X direction, we will divide that 2 UP spaces by the slope.

 

2/(-3/2) = -4/3  = -1 1/3.

 

Now we know we need to move 1 1/3 spaces to the left.  The X coordinate associated with the -5 we picked is 2.  When we move 1 1/3 spaces to the left, we end up at +2/3.

 

X = 2/3