Expert: Chanda Walker - 1/6/2009

Question
Write an equation of the line that passes through the given points.

1. (1,4),(2,7)

Answer
Jon, no problem!  It is my pleasure to help.

To construct the equation for a line, let's use the general form of a line

y = m x + b

where m is the slope of the line and b is the y intercept.

I'll solve for the slope first.

m = (y_2 - y_1)/(x_2 - x_1)
m = (7 - 4)/(2 - 1)
m = 3/1 = 3

Now let's put that back into the equation.

y = 3 x + b

We still need to solve for the intercept, b.  To do this let's pick one of the points given and substitute that in for x and y and solve for b.  I'll use (1, 4).

4 = 3 (1) + b
b = 4 - 3
b = 1

Putting it all together we get

y = 3 x + 1

Before we are finished we should check it!  To check it we will put the OTHER point in there and see if the equation holds true.

7 ? 3 (2) + 1
7 ? 6 + 1
7 = 7   Yep!  It is correct.

Ok so our solution for the line is:
y = 3 x + 1.

Hope this helps.  Feel free to ask more questions if you need further clarification.