Question

Find the equation of the line through the points (2,5) and (3,10) use function notation

Answer 1

f(x) = 5x - 5

Explanation:

the equation of a line in slope- intercept form is

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

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (2, 5 ) and (x₂, y₂ ) = (3, 10 )

m =
`(10-5)/(3-2)` =
`(5)/(1)` = 5 , then

y = 5x + c ← is the partial equation

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

using (2, 5 )

5 = 5(2) + c = 10 + c ( subtract 10 from both sides )

- 5 = c

y = 5x - 5 , that is

f(x) = 5x - 5 ← in function notation