Question

Write the equation of the line in slope-intercept form that passes through the points (-1, -2) and (4,23).

Answer 1

y = 5x + 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 ) = (- 1, - 2 ) and (x₂, y₂ ) = (4, 23 )

m =
`(23-(-2))/(4-(-1))` =
`(23+2)/(4+1)` =
`(25)/(5)` = 5 , then

y = 5x + c ← is the partial equation

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

Using (4, 23 ) , then

23 = 20 + c ⇒ c = 23 - 20 = 3

y = 5x + 3 ← equation of line