Describe what the slope and y intercept mean?

Question

 Brendan Bought 10 donuts. He eats 2 a day. Write an equation to represent the number of donuts he has. Label the slope and y intercept. Describe what the slope and y intercept mean. (3)

Answer 1

The y-intercept is your y-value on Day 0, the day Brendan buys 10 donuts, so the y-intercept is 10.

If he eats 2 donuts per day, that's a slope of -2 because he is DOWN 2 donuts every day. Yum!

y = mx + b, where m = the slope and b = the y-intercept...

y = -2x + 10

This looks backward, doesn't it? If he starts with 10 donuts and eats 2 a day, shouldn't it be 10 - 2x? Well, math is weird sometimes, and the slope with the independent variable (-2x in this case) comes before the constant (10), so there ya go!

Answer 2

In this particular case, when graphing this you would make the y-axis the number of donuts Brendan has on any day and the x-axis would be the number of days. On day "0", the day Brendan bought the donuts, the number of donuts he would have would be 10, or the y-intercept. Each subsequent day he would have 2 less donuts, which would be the slope, or b, of the line. You would graph this with these points: (0,10), (1,8), (2,6), (3,4), (4,2), (5,0). Putting this into an equation you would get

y = mx + b

y = -2x + 10

I hope this helps!