Question

In the piece-wise function graphed below, which is the correct equation for when − 2 ≤ x ≤ 2

Answer 1

Answer:

y=-1/2x+2

Step-by-step explanation:

y = mx + p

m=slope = -1/2

p= y-intercept = 2

Answer 2

Answer:

y = - $\frac{1}{2}$ x + 2

Step-by-step 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 = $\frac{1-3}{2+2}$ = $\frac{-2}{4}$ = - $\frac{1}{2}$

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

y = - $\frac{1}{2}$ x + 2 ← equation for - 2 ≤ x ≤ 2