Question

Jordan uses the following equation to determine how much she is paid for her babysitting services:c=13h+10What is the constant rate of change? What is the initial value?

Answer 1

Solution:

Given:

$c=13h+10$

where;

$\begin{gathered} c\text{ is the cost received for baby sitting services} \\ h\text{ is the number of hours spent} \end{gathered}$

The equation given is a linear equation.

This can be compared to the general form of a linear equation,

$\begin{gathered} y=mx+c \\ \text{where m is the rate of change or the slope} \\ c\text{ is the y-intercept} \end{gathered}$

Part A:

Comparing the two equations,

$\begin{gathered} c=13h+10 \\ y=mx+c \\ m=13 \\ c=10 \\ \\ \text{Hence, the rate of change (m)=13} \end{gathered}$

Therefore, the constant rate of change is 13.

This means Jordan receives 13$ for every hour spent babysitting.

Part B:

The initial value means the output value when the input value is zero.

From the equation, that is, the value of c when h =0

$\begin{gathered} c=13h+10 \\ \text{when h=0} \\ c=13(0)+10 \\ c=0+10 \\ c=10 \end{gathered}$

Therefore, the initial value is 10.