Question

In the piece-wise function graphed below, which is the correct equation for when -2 ≤ x ≤ 0

Answer 1

Answer:

y = 3x + 5

Step-by-step explanation:

In the interval - 2 ≤ x ≤ 0 the graph 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 )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

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

m = $\frac{5+1}{0+2}$ = $\frac{6}{2}$ = 3

The line intercepts the y- axis at (0, 5) ⇒ c = 5

y = 3x + 5 ← equation for - 2 ≤ x ≤ 0