Question

Write the equation for a line that intersects points (1,3) and (2,5).

Answer 1

y - 3 = 2 (x - 1)

OR

y = 2x + 1

Explanation:

First, find the slope (m):

m =
`(y2-y1)/(x2-x1)`

m =
`(5-3)/(2-1)` =
`(2)/(1)` = 2

Point-slope form: y - y1 = m (x-x1)

Plug in the numbers:

y - 3 = 2 (x - 1)

Slope intercept form: y = mx + b

For this, you need to find b (the y-intercept). You can do this by plugging in (1, 3) and then isolating b:

3 = 2(1) + b

3 = 2 + b

1 = b

Therefore:

y = 2x + 1