George plans to order flowers for his daughter’s graduation. A bouquet of 12 roses will cost $61, while a bouquet of 18 roses will cost $79. What is the equation that represents the linear relationship between price and the number of roses?

George plans to order flowers for his daughters graduation A bouquet of 12 roses will cost 61 while a bouquet of 18 roses will cost 79 What is the equation that class=


Answer :

Start by finding the slope of the line that passes through both the 12 roses bouquet and the 18 roses bouquet.

point 1: (12,61)

point 2: (18,79)

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ then, \\ m=\frac{79-61}{18-12} \\ m=\frac{18}{6} \\ m=3 \end{gathered}[/tex]

then, using one of the points find the fixed costs

[tex]\begin{gathered} P=m\ast r+b \\ using\text{ \lparen12,61\rparen} \\ 61=3\ast12+b \\ 61-36=b \\ b=25 \end{gathered}[/tex]

Answer:

The general equation that represents the linear relationship is:

[tex]P=25+3r[/tex]