Question

Complete the point-slope equation of the line through (2,3) and (7,4)
y-4=

Answer 1

y - 4 =
`(1)/(5)`(x - 7)

Explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (7, 4)

m =
`(4-3)/(7-2)` =
`(1)/(5)`

Use either of the 2 points for (a, b)

Using (7, 4), then

y - 4 =
`(1)/(5)`(x - 7) ← in point- slope form