Question

What is the equation of the line passing through (2,3) and (5,6)

Answer 1

y = mx + b

m = y2 - y1/x2 - x1
= 6 - 3 / 5 - 2
= 3/3= 1
y = x + b
(3) = (2) + b

1 = b

Answer: y = x + 1

Answer 2

y = x + 1

Explanation:

The equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (5, 6)

m =
`(6-3)/(5-2)` =
`(3)/(3)` = 1

y = x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (2, 3 ), then

3 = 2 + c ⇒ c = 3 - 2 = 1

y = x + 1 ← equation of line