Question

Find the equation of the line that passes through points A and B.

y
X A (4, 7)
B (2, 3)

Answer 1

y - 3 = 2(x - 2)

Explanation:

As we move from Point B (2, 3) to Point A (4, 7), we see x increasing by 2 from 2 to 4 and y increasing by 4 from 3 to 7. Hence the rise is 4 and the run is 2, which means that the slope of this line is m = rise / run = 4/2 = 2.

Using the point-slope formula y - k = m(x - h) and the point (2, 3), we get:

y - 3 = 2(x - 2)

Answer 2

y = 2x - 1.

Explanation:

The slope = (7-3)/(4-2)

= 4/2

= 2.

y - y1 = m(x - x1)

Here m = 2 , x1 = 2 and y1 = 3. So we have:

y - 3 = 2(x - 2)

y = 2x - 4 + 3

y = 2x - 1.

We have used the point (2, 3) to find the equation but we could have used (4, 7). We would have got the same answer.