You are using 0.05 gallons per mile of a SUV gas tank that holds 16 gallons. Note: this equation has a negative slope (m). Use x-values: 0, 160, and 320. I think the problem should be y=.05x+16 Confused since the teacher says it has a negative slope.
If you are computing the volume of gas in the tank vs miles driven, then naturally as the miles go up, the gas goes down.
Try y = 16 - .05x
If the equation for the gas consumption of your SUV is y = 0.05x + 16, then you are correct in stating that the slope (m) is positive. This means that as the x-values increase, the y-values also increase. However, if your teacher stated that the equation has a negative slope, there might be a mistake in either the equation or the given information.
To confirm, let's calculate the gas consumption for the given x-values using the equation y = 0.05x + 16:
1. For x = 0:
y = 0.05(0) + 16
y = 16
2. For x = 160:
y = 0.05(160) + 16
y = 8 + 16
y = 24
3. For x = 320:
y = 0.05(320) + 16
y = 16 + 16
y = 32
As you can see, the y-values increase with increasing x-values, indicating a positive slope. Therefore, it seems that the equation y = 0.05x + 16 is correct, and the gas consumption increases as the distance traveled (x) increases.
To determine whether the equation y = 0.05x + 16 has a positive or negative slope, we need to analyze the coefficient of x.
In this case, the coefficient of x is 0.05. Since this value is positive, the slope is indeed positive. Therefore, the equation y = 0.05x + 16 has a positive slope.
If you want to represent the situation with a negative slope, you'll need to change the coefficient of x to a negative value. For example, if the SUV was consuming less gas per mile as the distance increased, you could use a value like -0.05.
The modified equation would be: y = -0.05x + 16.
Now, let's calculate the y-values for the given x-values of 0, 160, and 320.
For x = 0, the equation becomes: y = -0.05(0) + 16 = 16. So, when there is no distance traveled (x = 0), the gas tank holds 16 gallons (y = 16).
For x = 160, the equation becomes: y = -0.05(160) + 16 = 8. So, when traveling 160 miles, the gas tank holds 8 gallons.
For x = 320, the equation becomes: y = -0.05(320) + 16 = 0. So, when traveling 320 miles, the gas tank will be empty (y = 0).
I hope this clarifies the confusion between positive and negative slopes in the equation.