please help me okay

Question

For each situation, determine the slope and 

y-intercept

 of the graph of the equation that describes the situation.

John gets a new job and receives a $600 signing bonus. After that, he makes $300 a day.

the slope is

The 

y-intercept

 is 

Answer 1

Let's take the info we have and do our best to picture in our minds what a graph like this would look like.

We know John starts off with $600 when he starts the job. Any amount of money John makes at his job will be added to that $600 he had to begin with. This is a starting amount of money for John. He does not make an additional $600 each time he goes back to work.

Now we look at John's wage. He makes $300 per day at this job.It is useful to know that a wage is a rate of change over time. In simpler terms, that means John will be getting the same amount of money each day he goes into work which will add to John's total amount of money over time. We will assume John goes to work every day to make understanding this problem easier.

So we know that John has an amount of money he began with, and he also has a certain amount of money that he also gets every day. Those amounts of money relate to a slope and a y-intercept if they were put on a graph.

If we took Joe's amount of money over time and put it into a graph, we would need to understand what amount of money John has at the start of time. Consider a graph that has a horizontal axis related to time in days, and a vertical axis related to John's total amount of money.

At a time t = 0, or 0 days, John has $600 at the time he gets a bonus before day 1 of work. The amount of money that John has at t = 0 is the y-intercept of this graph.

Over time, John's amount of money goes up by $300 per day. We refer to this as the slope of the graph.

Since we know our y-intercept and slope to graph John's amount of money over time, we can turn it into a linear equation in the form:

y = m*t + b

where m is the slope, b is the y-intercept, and t represents the time in days John has worked.

We already know:

m = 300

b = 600

Now let's put it together:

y = 300*x + 600

I'm going through the steps of making this equation to give you a better understanding of why we look at the $600 as the y-intercept and the $300 as the slope.

I hope this was useful!

Answer 2

Let x = number of days that John works and y = amount of money he gets after working for x days.

Then, y = 300x + 600

Slope = 300 and y-intercept = 600