Please help me with this i filled in the points but i am so lost, sorry i can't show the graph on here
3. Plot 2 ordered pairs on the initial climb (first part of the rollercoaster going up) and determine the slope.
Points:(10,20)and (30,60)Work to find Slope: Slope: ________
4. What is the equation of the line in slope-intercept form that represents your initial climb (first part of the rollercoaster going up)?
Equation: ___________
5. What is the domain and range of your entire roller coaster? (HINT: use compound inequalities)
Domain: Range:
6. a) Plot 2 ordered pairs at the top and the bottom of each hill (not the loop).
Hill 1 points: (0,0) and (130,260) Hill 2 points:(170,60) and (130,260)
b) Find the rate of change going down each hill.
Work for Hill 1: Work for Hill 2:
Rate of change down Hill 1: _______ Rate of change down Hill 2: _______
c) Which hill is steeper? How do you know that hill is steeper?
Hill 1 or Hill 2 (circle/underline/pick one)
Explanation:
7. Is the roller coaster a function? Why or why not?
Function: YES or NO (circle/underline/pick one)
Explanation:
3. To find the slope of the initial climb, you need to use the formula for slope, which is (change in y)/(change in x). Let's use the points (10,20) and (30,60).
First, calculate the change in y: 60 - 20 = 40.
Then, calculate the change in x: 30 - 10 = 20.
Now, substitute these values into the slope formula: slope = (change in y)/(change in x) = 40/20 = 2.
Therefore, the slope of the initial climb is 2.
4. To find the equation of the line in slope-intercept form, we can use the slope we found in the previous step (which is 2) and one of the points on the line. Let's use the point (10,20).
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Substitute the slope (m) and the point (x,y) into the equation: 20 = 2(10) + b.
Now, solve for b: 20 = 20 + b.
Therefore, b = 0.
The equation of the line in slope-intercept form is y = 2x + 0, which simplifies to y = 2x.
5. To determine the domain and range of the entire roller coaster, we need to consider all the points on the roller coaster.
The domain is the set of all possible x-values. In this case, it depends on the starting and ending points of the roller coaster graph, and any restrictions mentioned in the problem. Without a graph, it is difficult to determine the exact domain.
The range is the set of all possible y-values. It depends on the highest and lowest points of the roller coaster graph, and any restrictions mentioned in the problem. Without a graph, it is difficult to determine the exact range.
6. a) You need to plot two ordered pairs at the top and the bottom of each hill. Let's use the given points for Hill 1 and Hill 2:
Hill 1 points: (0,0) and (130,260)
Hill 2 points: (170,60) and (130,260)
b) To find the rate of change going down each hill, you need to calculate the slope using the same formula as in step 3. Use the given points for Hill 1 and Hill 2.
For Hill 1: slope = (change in y)/(change in x) = (260 - 0)/(130 - 0).
For Hill 2: slope = (change in y)/(change in x) = (260 - 60)/(130 - 170).
c) To determine which hill is steeper, compare the calculated slopes from step 6b. The hill with the greater absolute value of slope (ignoring the positive or negative sign) is steeper.
7. To determine if the roller coaster is a function, we need to see if each input (x-value) has only one output (y-value). Without the graph or more information, it is difficult to determine if the roller coaster is a function.
Explanation: A function is a set of ordered pairs where each x-value is associated with only one y-value. If there are any points on the graph where multiple y-values are associated with the same x-value, then the roller coaster would not be a function.