Question

Write the equation of the line in slope-intercept form.

11. A line that passes through (3, 1) and (0, -3)

Answer 1

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

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 ) = (3, 1) and (x₂, y₂ ) = (0, - 3)

m =
`(-3-1)/(0-3)` =
`(-4)/(-3)` =
`(4)/(3)`

The line crosses the y- axis at (0, - 3) ⇒ c = - 3

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

Answer 2

y=(4/3)x - 3

Explanation:

Use equation (y-y1) =m (x-x1)

slope is m= (y1-y2)/(x1-x2)=1+3/3-0=4/3

use one of the points and this slope to complete the equation

(y-1)=(4/3)(x-3) distribute and add1 to both sides

y=(4/3)x-(3*4/3)+1

y=(4/3)x - 3