Question

The function f(x) is shown in this graph.

5
(0,2)
The function g(x) = -3x - 6. Compare the slopes,
Help plz

Answer 1

The slopes are equal

Explanation:

Calculate the slope m of f(x) using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (0, 2) ← 2 points on the line

m =
`(2-5)/(0-(-1))` =
`(-3)/(0+1)` =
`(-3)/(1)` = - 3

The equation of a line in slope- intercept form is

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

g(x) = - 3x - 6 ← is in slope- intercept form

with slope m = - 3

Then the slopes of f(x) and g(x) are equal, meaning the lines are parallel