Answer:
7. a) 1/2
b) 18
8. 2/3 lpm (see below)
Step-by-step explanation:
For No. 7, part A, finding the slope is simple. Just use the slope formula:
y2 - y1
m = ------------
x2 - x1
Now, choose any two points and plug them in. I'm using (2, 1) and (6, 3):
3 - 1
m = ---------
6 - 2
2
m = ---- = 1/2
4
Slope is the steepness of this line. It's made up of rise (y) over run (x). So in this case, this line will always go up by one unit and right two units.
To solve for part B, you can write an equation in slope-intercept form. To do this, you'll need the y-intercept, which is the point where the line meets the y-axis.
So in this case, it'll be (0, 0), meaning the y-intercept is 0.
Using;
y = mx + b
You can plug in the slope, y-intercept, and 9 as the y (because she makes 9 cups of yogurt, which is the y-axis, and you're trying to find x)
9 = 1/2x + 0
Simplify:
9 = 1/2x
9 (2) = 1/2x (2)
18 = x
x = 18
So, she uses 18 berries in 9 cups of yogurt.
For No. 8, it's a simple mix-up with slope:
Slope is the change in y over the change in x, which means rise/run. She did the opposite: change in x over change in y.
The correct answer would be:
2/3 ≈ 0.67
So she would be going at 2/3 (or about 0.7) lpm (laps per minute).
