In the piece-wise function graphed below, which is the correct equation for when − 2 ≤ x ≤ 2 y=-2x+2 y=-1/2x+2 y=-2x+4 y=-1/2x+4

Question

asked Oct 20, 2021 21.1k views

2 Answers

Martin Baumgartner · Answer 1 · 2021-10-21T03:16:50+0000

Answer:

y = -
(1)/(2) x + 2

Explanation:

The segment for - 2 ≤ x ≤ 2 is a straight line

The equation of a line in slope- intercept form is

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

To calculate m use the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (2, 1) ← the endpoints of the line

m =
(1-3)/(2+2) =
(-2)/(4) = -
(1)/(2)

Note the line crosses the y- axis at (0, 2) ⇒ c = 2

y = -
(1)/(2) x + 2 ← equation for - 2 ≤ x ≤ 2