Question

Determine the intercepts of the line that correspond to the following table of values.

x | y
-15| -1
-9 | -3
-3 | -5

x-intercepts _-0
y-intercepts 0-_

Answer 1

x-intercept (- 18, 0 ), y-intercept(0, - 6 )

Find the equation of the line in slope-intercept form

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

to calculate m use the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 15, - 1 ) and (x₂, y₂ ) = (- 3, - 5 )

m =
`(-5+1)/(-3+15)` =
`(-4)/(12)` = -
`(1)/(3)`

y = -
`(1)/(3)` x + c ← is the partial equation

To find c substitute (- 3, - 5 ) into the partial equation

- 5 = 1 + c ⇒ c = - 6

y = -
`(1)/(3)` x - 6 ← equation in slope-intercept form

with y- intercept = - 6 ⇒ (0, - 6)

to find the x-intercept let y = 0, in the equation and solve for x

y = 0 : -
`(1)/(3)` x - 6 = 0 ⇒ x = - 18

hence x-intercept = - 18 ⇒ (- 18, 0 )