Math CentralQuandaries & Queries


Question from Jennifer, a student:

Given the point A(3,2) B(5,8) find the equation of the line AB ( in standard form )

Hi Jennifer,

I am going to use different points, A(3, -2) and B(7, 6) . I would first use the points to find the slope of the line

slope = m = (difference in the y coordinates)/(difference in the x coordinates)
= [6 - (-2)]/[7 - 3] = 8/4 = 2

Now that I have the slope there are two expressions I could use to find the equation of the line

(y - y1) = m (x - x1) or
y = m x + b

To use the first form, the point slope form, I would choose one of the two points A or B and substitute its coordinates for x1 and y1. To use the second form, the slope intercept for, choose one of the points A or B, substitute its coordinates for x and y and then solve for b. I'm going to use the point slope form and use the point B. Thus I get

(y - 6) = 2 (x - 7)

The standard form of a line is

Px + Qy = c

so I need to manipulate (y - 6) = 2 (x - 7) into this form. Multiplying the 2 through the parentheses on the right I get

y - 6 = 2x - 14

Finally add 6 to each side and subtract 2x from each side to get

-2x + y = -8

Now try this with the points you were given,

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