Question

What is an equation of the line that passes through the points (1,-1) and (3,7)?

Answer 1

y = 4x - 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 ) = (1, - 1 ) and (x₂, y₂ ) = (3, 7 )

m =
`(7-(-1))/(3-1)` =
`(7+1)/(2)` =
`(8)/(2)` = 4 , then

y = 4x + c ← is the partial equation

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

using (3, 7 ) , then

7 = 4(3) + c = 12 + c ( subtract 12 from both sides )

- 5 = c

y = 4x - 5 ← equation of line