Answer:
C
Step-by-step explanation:
The function is formed of 2 straight lines
The equation of a straight line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate the slope using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 4, - 5) and (x₂, y₂ ) = (2, - 2) ← endpoints of left line
m = [tex]\frac{-2+5}{2+4}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
Note the line crosses the y- axis at (0, - 3) ⇒ c = - 3
y = [tex]\frac{1}{2}[/tex] x - 3 for x < 2 ( arrow on line points left )
Repeat
with (x₁, y₁ ) = (2, - 2) and (x₂, y₂ ) = (3, 1) ← 2 points on right line
m = [tex]\frac{1+2}{3-2}[/tex] = [tex]\frac{3}{1}[/tex] = 3, thus
y = 3x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (3, 1), then
1 = 9 + c ⇒ c = 1 - 9 = - 8
y = 3x - 8 for x ≥ 2 ( arrow on line points right )
