Question

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

Answer 1

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

Answer 2

y=-1/2x+2

Explanation:

y = mx + p

m=slope = -1/2

p= y-intercept = 2