Answer:
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).
Step-by-step explanation:
To solve this question we shall look at linear equations of the simplest form reading:
[tex]y = mx+c[/tex] Eqn(1).
where:
[tex]y[/tex]: is our dependent variable that changes as a function of x
[tex]x[/tex]: is our independent variable that 'controls' our equation of y
[tex]m[/tex]: is the slope of the line
[tex]c[/tex]: is our y-intercept assuming an [tex]x[/tex]⇔[tex]y[/tex] relationship graph.
This means that as [tex]x[/tex] changes so does [tex]y[/tex] 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:
[tex]c=300[/tex]
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:
[tex]m=50[/tex]
So finally we have the following linear equation of:
[tex]y= - 50x + 300[/tex] 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 [tex]x[/tex] values we have:
Week 1: [tex]x=1[/tex] we have [tex]y= -50 *1 + 300 = -50 +300 = 250[/tex] dollars.
Week 2: [tex]x=2[/tex] we have [tex]y= -50 *2 + 300 = -100 +300 = 200[/tex] dollars.
Thus having understood the above we can comment on the questions asked as follow:
Part c)
The Slope of the line is: [tex]m=-50[/tex] and represents the amount of money spent per week.
Part d)
The y-intercept is: [tex]c=300[/tex] and represents the maximum money we have that can be spend over the weeks (i.e. our maximum budget alowed).
