MATH SOLVE

2 months ago

Q:
# 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?

Accepted Solution

A:

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).