Question

Write an equation for the line that passes through (4, -5) and (3, -2)

Answer 1

y = - 3x + 7

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, - 5 ) and (x₂, y₂ ) = (3, - 2 )

m =
`(-2-(-5))/(3-4)` =
`(-2+5)/(-1)` =
`(3)/(-1)` = - 3 , then

y = - 3x + c ← is the partial equation

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

using (3, - 2 )

- 2 = - 3(3) + c = - 9 + c ( add 9 to both sides )

7 = c

y = - 3x + 7 ← equation of line