Question 1
The graph shows the diagonal line crossing the vertical y axis at 8. So the y intercept is 8. This is the starting height because x = 0 here. The slope of the line determines the speed. Why? Recall that the slope is the rise over run
slope = rise/run
slope = (change in y)/(change in x)
slope = (change in height)/(change in time)
When we divide a change in height, or basically a distance, over a change in time, then we end up with a speed value. For instance, let's say the flag goes up 10 feet in 2 seconds. That speed would be 10/2 = 5 feet per second.
The graph shows that when we go up 8 units on the y axis, and also go to the right 4, then we move from (0,8) to (4,16). The slope for this graph would be
slope = rise/run = 8/4 = 2
So the slope is 2
We can use the slope formula to get this same slope answer
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Question 2
The equation h = 8 + 2t is the same as h = 2t + 8. Adding two numbers can be done in any order, which is why 8+2t is the same as 2t+8.
Then we'll do two replacements. Replace t with x, and replace h with y. We end up with y = 2x+8. Note how it's in the form y = mx+b
m = slope
b = y intercept
Since m = 2, the slope is 2. Since b = 8, the y intercept is 8.
The slope of 2 corresponds directly to the speed, as mentioned back in question 1 above. The y intercept being the starting height is also explained back in the previous problem.
