Question

You saved $300 to spend over the summer. You decide to budget $50 to spend each week.

Part c: what is the slope of the line? What does the slope represent?
Part D: what is the y-intercept? What does this point represent?

Answer 1

Part c)

The Slope of the line is: m=-50 and represents the amount of money spent per week.

Part d)

The y-intercept is: c=300 and represents the maximum money we have that can be spend over the weeks (i.e. our maximum budget alowed).

Explanation:

To solve this question we shall look at linear equations of the simplest form reading:

`y = mx+c` Eqn(1).

where:

`y`: is our dependent variable that changes as a function of x

`x`: is our independent variable that 'controls' our equation of y

`m`: is the slope of the line

`c`: is our y-intercept assuming an
`x`⇔
`y` relationship graph.

This means that as
`x` changes so does
`y` as a result.

Given Information:

Here we know that $300 is our Total budget and thus our maximum value (of money) we can spend, so with respect to Eqn (1) here:

`c=300`

The budget of $50 here denotes the slope of the line, thus how much money is spend per week, so with respect to Eqn (1) here:

`m=50`

So finally we have the following linear equation of:

`y= - 50x + 300` Eqn(2).

Notice here our negative sign on the slope of the line. This is simply because as the weeks pass by, we spend money therefore our original total of $300 will be decreasing by $50 per week.

So with respect to Eqn(2), and different weeks thus various
`x` values we have:

Week 1:
`x=1` we have
`y= -50 *1 + 300 = -50 +300 = 250` dollars.

Week 2:
`x=2` we have
`y= -50 *2 + 300 = -100 +300 = 200` dollars.

Thus having understood the above we can comment on the questions asked as follow:

Part c)

The Slope of the line is:
`m=-50` and represents the amount of money spent per week.

Part d)

The y-intercept is:
`c=300` and represents the maximum money we have that can be spend over the weeks (i.e. our maximum budget alowed).