Expert: Bobby Soltani - 11/3/2005

Question
A line counting the points (9,1) and (5,5) intersects the x-axis at what point?

Answer
Hi Ashley,

There are several ways to solve this.  Here's one.

point 1 (x1,y1) = (9,1)
point 2 (x2,y2) = (5,5)

the equation for a line is
y-y1 = m(x-x1)
where m = (y2-y1)/(x2-x1) = (5-1)/(5-9) = -1

So the equation for the line is

y - 1 = -1(x - 9)
y - 1 = -x + 9
y = -x + 10

we want to know where the line intersects the x axis.  At the x-axis the value of y is zero.  So we can set the y=0 in the equation for the line and solve for x.

0 = -x + 10
x = 10

Let me know if you have any questions.

Bobby