Answer:
B
Step-by-step explanation:
It is linear.
We can see the right side are multiples of 3. So the equation so the table is:
c = 3h
When h = 5 c = 15
c = 3h
c = 3*5
c = 15
When h = 12 c = 36
c = 3h
c = 3*12
c = 36
The constant rate of change between cost and time is 3.
Another way to solve is check for rate of change using 2 points on the chart.
Let's choose h = 5 c = 15 and h = 12 c = 36
The normal equation for rate of change is:
m = [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex] in this case we have h and c so:
[tex]\frac{c_{2} -c_{1}}{h_{2}-h_{1}}[/tex]
h₁ = 5 h₂ = 12
c₁ = 15 c₂ = 36
So:
[tex]\frac{c_{2} -c_{1}}{h_{2}-h_{1}} = \frac{36 -15}{12-5} = \frac{21}{7} = \frac{3}{1} =3[/tex]
Now that we know it's 3 we use slope intercept form to find the equation.
y = mx + b ( m = 3) and we plug in a point to find b.
y = 3x + b h = 5 (x) c = 15 (y)
15 = 3(5) + b Solve for b.
15 = 15 + b Subtract 15 from each side.
15 - 15 = 15 - 15 + b
0 = b b is 0 showing our equation was correct.
y = 3x or c = 3h
