Which graph below shows the rule: output = 4 times input?

(I am unable to put graphs in.)

Write a rule for the function represented by the table
0, 13
1, 28
2, 43
3, 58

A. y = 15 + 13x
B. y = 14 + 12x
C. y = 13 + 15x**
D. y = 12 + 14x

Select a graph for the situation. On a trip, the gas mileage remains constant when traveling between 10 and 20 miles per hour, increases until speeds reach 50 mph, and then decreases as the speed increases.

(Once again, I cannot show the graphs.)

Uh. What about the actual multiple-choice answer?

I'm sorry, since I can't see the graphs you mentioned, I'll have to resort to using humor instead.

For the first question, since I can't view the graphs, I guess multiplying the input by four could be graphed as a mountain, a roller coaster, or maybe even a pogo stick. It's all about that upward trend!

As for the second question, imagine a graph that looks like a zigzag. It speeds up, slows down, and then speeds up again, just like the gas mileage on a road trip. It's like driving through a funhouse, but without the clowns. Well, hopefully without the clowns.

Remember, laughter is the best fuel for understanding!

For the first question, the graph that represents the rule "output = 4 times input" is the one with a straight line that passes through the origin and has a slope of 4. It will show a constant increase in the output as the input increases.

For the second question, the rule for the function represented by the table can be determined by looking for a pattern in the given values. In this case, as the input increases by 1, the output increases by 15. Therefore, the rule for the function is y = 13 + 15x. So the correct answer is C.

For the third question, since the gas mileage remains constant between 10 and 20 mph, the graph should have a horizontal line segment in that range. As the speed increases beyond 20 mph, the gas mileage increases, so the graph should slope upwards. However, once the speed reaches 50 mph, the gas mileage starts to decrease as the speed increases further. Therefore, the correct graph would have an increasing slope until 50 mph and then a decreasing slope after that point.

To determine which graph shows the rule "output = 4 times input," you need to look for a linear equation of the form y = 4x, where x represents the input and y represents the output.

Unfortunately, without being able to see the graphs, it's challenging to identify the specific graph that satisfies the given rule. However, you can use some key characteristics to help you identify the correct graph:

1. Look for a straight line: The graph should be a straight line because the equation given is a linear function.

2. Check the slope: The slope of the line should be 4. The slope represents the rate of change, which indicates how much the output (y) changes for every unit increase in the input (x). In this case, the slope needs to be 4 for the rule "output = 4 times input" to hold true.

3. Look for the y-intercept: The y-intercept is the value of y when x is zero. If the rule is "output = 4 times input," the y-intercept should be zero since 0 multiplied by any number is zero.

Examine the equations in the answer choices and determine which one satisfies the characteristics mentioned above.

For the second question regarding the rule represented by the table, you can find the rule by observing the pattern in the data provided.

By looking at the table, you can notice that for every increase of 1 in the input, the output increases by 15. This suggests that the rule has a constant rate of change, meaning the output increases by the same amount each time the input increases by 1.

To find the equation, you can use the slope-intercept form of a linear equation (y = mx + b). In this case, m represents the slope (rate of change) and b represents the y-intercept.

Using the given data points, we can calculate the slope:
Slope (m) = (Change in y) / (Change in x)
Slope (m) = (28 - 13) / (1 - 0) = 15

Since the slope is 15, we can conclude that the equation for the function represented by the table is: y = 15x + b.

To find the y-intercept (b), we can substitute one of the points into the equation and solve for b. Let's use the first data point (0, 13):
13 = 15(0) + b
13 = b

Therefore, the equation for the function represented by the table is y = 15x + 13. Comparing this equation to the answer choices, we can see that the correct option is C: y = 13 + 15x.

As for the third question about selecting a graph, since we can't see the available graphs, we need to describe the characteristics of the gas mileage situation.

The given information states that gas mileage remains constant between 10 and 20 mph, increases until reaching 50 mph, and then decreases as the speed increases.

Based on this description, the graph should show a constant value of gas mileage between 10 and 20 mph, a positive slope leading up to 50 mph, and then a negative slope after 50 mph.

Without visualizing the graphs, you will need to analyze the options and determine which one satisfies these characteristics. Look for a graph that has a constant flat line between 10 and 20 mph, an increasing slope leading up to 50 mph, and a decreasing slope thereafter.

Remember, since I am unable to see the graphs, my explanation is based on the information provided.

C. y = 13 + 15x**

Yes