The capacity of the gas tank in a car is 16.5 gallons. The car uses 10.5 gallons to travel 178.5 miles. After driving 85 more miles, only 1 gallon of gasoline remains in the tank. Which linear equation and graph model the amount of gas g left in the tank after driving m miles?
178.5mi/10.5gal = 17 mi/gal
This is consistent with 85mi/5gal, so
g(m) = 16.5 - m/17
Well, let's start with the equation:
Since the car starts with 16.5 gallons and uses 10.5 gallons to travel 178.5 miles, we can find the rate at which gas is consumed:
Rate of gas consumption = 10.5 gallons / 178.5 miles = 0.059 gallons/mile
Therefore, the equation that represents the amount of gas left in the tank after driving m miles is:
g = 16.5 - 0.059m
Now, let's take this equation for a spin on a graph:
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Voila! There you have it - a linear equation and graph modeling the amount of gas left in the tank after driving m miles, with a touch of clownish flair.
To determine the linear equation that models the amount of gas left in the tank, we need to find the rate at which gasoline is being consumed.
Given that the car uses 10.5 gallons of gas to travel 178.5 miles, we can find the rate of gasoline consumption:
Rate = Amount of gas used / Distance traveled
Rate = 10.5 gallons / 178.5 miles
Rate ≈ 0.0588 gallons/mile
Using this rate, we can determine the amount of gas remaining in the tank after driving a certain number of miles.
Let's represent g as the amount of gas remaining in the tank and m as the number of miles driven. We want to find the linear equation that relates g and m.
The initial amount of gas is 16.5 gallons, and after driving 10.5 gallons are used, leaving 6 gallons in the tank. So, we have the point (0, 16.5) and (178.5, 6) on the graph.
Using the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept, we can determine the equation:
m = (change in y) / (change in x) = (6 - 16.5) / (178.5 - 0) = -0.056 (approximately)
Substituting this value of m into the equation, we get:
g = -0.056m + b
Using the point (0, 16.5) to find the y-intercept, we can solve for b:
16.5 = -0.056(0) + b
b = 16.5
Therefore, the linear equation that models the amount of gas left in the tank after driving m miles is:
g = -0.056m + 16.5
To graph the equation, we can plot the points (0, 16.5) and (178.5, 6), and then draw a straight line through them.
This graph will represent the amount of gas remaining in the tank after driving a certain number of miles.
To find the linear equation and graph that models the amount of gas left in the tank after driving a certain number of miles, we can use the given information.
Let's start by breaking down the problem step by step:
1. We know that the car's gas tank has a capacity of 16.5 gallons.
2. The car uses 10.5 gallons to travel 178.5 miles.
3. After driving 85 more miles, only 1 gallon of gasoline remains.
To find the linear equation that models the amount of gas left, we can use the slope-intercept form of a linear equation: y = mx + b, where y represents the amount of gas left, x represents the number of miles driven, m represents the slope, and b represents the y-intercept.
Since we have two points (178.5, 10.5) and (178.5 + 85, 1), we can use these points to find the equation.
Step 1: Find the slope (m):
The slope (m) represents the rate at which the gas is being used. We can find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (178.5, 10.5) and (178.5 + 85, 1):
m = (1 - 10.5) / (178.5 + 85 - 178.5)
m = -9.5 / 85
m = -0.111764706 (rounded to 9 decimal places)
Step 2: Find the y-intercept (b):
The y-intercept represents the initial amount of gas in the tank. Since we know that the tank's capacity is 16.5 gallons, we can assume that at x = 0 miles, the amount of gas left is 16.5 gallons.
Therefore, the y-intercept (b) is 16.5.
Step 3: Write the linear equation:
Using the slope-intercept form (y = mx + b) and substituting the values we found:
y = -0.111764706x + 16.5
This is the linear equation that models the amount of gas left in the tank after driving a certain number of miles.
To graph this equation, plot the x-axis for the number of miles and the y-axis for the amount of gas left in the tank.