Question

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

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 = $\frac{-5+1}{-3+15}$ = $\frac{-4}{12}$ = - $\frac{1}{3}$

y = - $\frac{1}{3}$ x + c ← is the partial equation

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

- 5 = 1 + c ⇒ c = - 6

y = -$\frac{1}{3}$ 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 : - $\frac{1}{3}$ x - 6 = 0 ⇒ x = - 18

hence x-intercept = - 18 ⇒ (- 18, 0 )