Question

Write the equation of the line that passes through (1,8) and (3, 3). Write it in slope-intercept form.

Answer 1

y = -
`(5)/(2)` x +
`(21)/(2)`

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 ) = (1, 8) and (x₂, y₂ ) = (3, 3)

m =
`(3-8)/(3-1)` = -
`(5)/(2)` , thus

y = -
`(5)/(2)` x + c ← is the partial equation

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

Using (1, 8), then

8 = -
`(5)/(2)` + c ⇒ c = 8 +
`(5)/(2)` =
`(21)/(2)`

y = -
`(5)/(2)` x +
`(21)/(2)` ← equation of line