Christa's distance from school is represented by y=-100x +1300. Stephen's distance from school is represented by y= -60x +1000.
Using the slope and y-intercept from each equation, find out who lives
farther from school and who walked to school faster.

Step-by-step explanation:

If you think of the y-axis is the "distance" axis (in feet for example), and the x-axis as the time axis (in minutes for example), then what you have is a velocity graph (velocity is the distance traveled divided by the time it takes to get there). If you haven't moved at all, your time is 0 (ON the y-axis) and the distance value (the y-intercept) is where you started. In other words, if no time has gone by, I haven't moved from my initial position yet. So the y-intercept of both of those equations serves as the intial distance each is from school.

In the equation y = mx + b, b is the y-intercept. The y-intercept in Christa's equation is 1300 (in feet) which means that before she leaves her house for school (no time has gone by yet), her initial distance from school is 1300 feet. Likewise, for Stephen. The y-intercept in his equation is 1000, so his initial distance from school is 1000 feet. Christa lives farther away than does Stephen.

Now for the rate they are each walking...

Rate is also (sort of the same thing as) velocity. It is represented in our equation by the m. In a "regular" slope-intercept equation, this would be the slope. Slope is the rate at which something is changing. Since our graph is a velocity graph--distance over time--our slope represents the distance each covers for every minute they walk. Christa's velocity is 100 feet per minute and Stephen's is 60 feet per minute. From this we can determine that Christa walks faster because she covers more feet per minute than does Stephen.

The equations are both negative because they are shortening their distances to the school. By this I mean that as they continue walking to school and the amount of time that goes by gets greater, the distance they are from the school gets smaller.

Hope this helps you understand what linear equations actually mean to the real world!

5x+2x=49

7x=49

x=7. 35 apples

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2