Question

What is the slope intercept form for the equation of the line
connecting (-4,1) and (4,7).

Answer 1

y =
`(3)/(4)` x + 4

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 ) = (- 4, 1 ) and (x₂, y₂ ) = (4, 7 )

m =
`(7-1)/(4-(-4))` =
`(6)/(4+4)` =
`(6)/(8)` =
`(3)/(4)` , then

y =
`(3)/(4)` x + c ← is the partial equation

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

using (4, 7 )

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

4 = c

y =
`(3)/(4)` x + 4 ← equation of line