Question

Write the slope intercept form for the equation of the line through the given points

(2,4) and (3,1)

Answer 1

y = - 3x + 10

Explanation:

the equation of a line in slope- intercept form is

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

calculate slope m using the slope formula

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

let (x₁, y₁ ) = (2, 4 ) and (x₂, y₂ ) = (3, 1 )

substitute these values into the formula for m

m =
`(1-4)/(3-2)` =
`(-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, 1 ) for x and y

1 = - 3(3) + c = - 9 + c ( add 9 to both sides )

10 = c

y = - 3x + 10 ← equation of line