Question

Ramona has a new job as à chef. She earns the sameamount per hour as she did in her old job, plus she got a$100 sign-on bonus. Line p represents Ramona's earnings inher old job. Line q represents her earnings in her new job.Write an equation for line p. What does the slope mean?How can you use the equation for line p to write anequation for line q?Amount

Answer 1

Using the graph of line p, we select two points in order to find the slope through the equation:

`m=(y_2-y_1)/(x_2-x_1)`

if we select points (0,0) and (4,40),

`\begin{gathered} m=(40-0)/(4-0) \\ m=(40)/(4) \\ m=10 \end{gathered}`

then, since the line passes through the point (0,0) the equation for line p is

`y=10x`

The meaning of the slope is the amount she earns per hour she works.

Since she earns the same on both jobs per hour worked, it means the slope of the line is the same in both cases, however, she hets a $100 bonus, which means that the resulting equation for q is:

`y=10x+100`

Answer:

- The equation of line p is: y=10x

- The slope means she earns $10 for every hour she works

- Both lines have the same slope, but line q has the bonus, meaning the equation is: y=10x+100