Question

Write an equation in slope-intercept form of the line that passes through (7, 2) and (2, 12).

y =

Answer 1

y = - 2x + 16

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 ) = (7, 2) and (x₂, y₂ ) = (2, 12)

m =
`(12-2)/(2-7)` =
`(10)/(-5)` = - 2, then

y = - 2x + c ← is the partial equation

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

Using (2, 12 )

12 = - 4 + c ⇒ c = 12 + 4 = 16

y = - 2x + 16 ← equation of line