(A ) This is a straight line graph.
The equation of a straight line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 1 ) and (x₂, y₂ ) = (-2, - 3 ) ← 2 points on the line
m = [tex]\frac{-3-1}{-2-0}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2
The y-intercept = (0, 1 ) ⇒ c = 1
f(x) = 2x + 1 ← function rule
(B)
To evaluate f(2), substitute x = 2 into the rule
f(2) = (2 × 2 ) + 1 = 4 + 1 = 5
As a check (2, 5 ) is a point on the graph
