QuestionGraph the linear function for Tim's truck fuel: $y = 200 - 10x$ , where $x$ is time in hours and $y$ is fuel in gallons.

Studdy Solution

STEP 1

Assumptions1. The truck starts with a full tank containing200 gallons of fuel. . For every hour Tim drives, the truck consumes10 gallons of fuel.
3. The relationship between the time driven and the remaining fuel is linear.

STEP 2

We can represent the relationship between the time driven and the remaining fuel as a linear function. The general form of a linear function is $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept.

STEP 3

In our case, the slope $m$ is the rate of fuel consumption, which is -10 gallons per hour. The negative sign indicates that the amount of fuel decreases as time increases.

STEP 4

The y-intercept $c$ is the initial amount of fuel, which is200 gallons.

STEP 5

So, the linear function representing the relationship between the time driven in hours (x) and the fuel remaining in the truck in gallons (y) is $y = -10x +200$ .

STEP 6

To graph this function, we start by plotting the y-intercept (0,200) on the graph.

STEP 7

Then, we use the slope to find other points on the graph. Since the slope is -10, this means that for every increase of1 hour in driving time, the amount of fuel decreases by10 gallons.

STEP 8

We can use the table given in the problem to find more points on the graph. For example, after5 hours of driving, there are150 gallons of fuel remaining. So, we plot the point (5,150) on the graph.

STEP 9

Similarly, we plot the points (,100) and (15,50) on the graph.

STEP 10

Finally, we draw a line through the points we have plotted. This line represents the linear function $y = -10x +200$ .

Was this helpful?

QuestionGraph the linear function for Tim's truck fuel: $y = 200 - 10x$ , where $x$ is time in hours and $y$ is fuel in gallons.

Studdy Solution

STEP 1

Assumptions1. The truck starts with a full tank containing200 gallons of fuel. . For every hour Tim drives, the truck consumes10 gallons of fuel.
3. The relationship between the time driven and the remaining fuel is linear.

STEP 2

We can represent the relationship between the time driven and the remaining fuel as a linear function. The general form of a linear function is $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept.

STEP 3

In our case, the slope $m$ is the rate of fuel consumption, which is -10 gallons per hour. The negative sign indicates that the amount of fuel decreases as time increases.

STEP 4

The y-intercept $c$ is the initial amount of fuel, which is200 gallons.

STEP 5

So, the linear function representing the relationship between the time driven in hours (x) and the fuel remaining in the truck in gallons (y) is $y = -10x +200$ .

STEP 6

To graph this function, we start by plotting the y-intercept (0,200) on the graph.

STEP 7

Then, we use the slope to find other points on the graph. Since the slope is -10, this means that for every increase of1 hour in driving time, the amount of fuel decreases by10 gallons.

STEP 8

We can use the table given in the problem to find more points on the graph. For example, after5 hours of driving, there are150 gallons of fuel remaining. So, we plot the point (5,150) on the graph.

STEP 9

Similarly, we plot the points (,100) and (15,50) on the graph.

STEP 10

Finally, we draw a line through the points we have plotted. This line represents the linear function $y = -10x +200$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionGraph the linear function for Tim's truck fuel: y=200−10xy = 200 - 10xy=200−10x, where xxx is time in hours and yyy is fuel in gallons.

Studdy Solution

STEP 1

Assumptions1. The truck starts with a full tank containing200 gallons of fuel. . For every hour Tim drives, the truck consumes10 gallons of fuel.3. The relationship between the time driven and the remaining fuel is linear.

STEP 2

We can represent the relationship between the time driven and the remaining fuel as a linear function. The general form of a linear function is y=mx+cy = mx + cy=mx+c, where mmm is the slope and ccc is the y-intercept.

STEP 3

In our case, the slope mmm is the rate of fuel consumption, which is -10 gallons per hour. The negative sign indicates that the amount of fuel decreases as time increases.

STEP 4

The y-intercept ccc is the initial amount of fuel, which is200 gallons.

STEP 5

So, the linear function representing the relationship between the time driven in hours (x) and the fuel remaining in the truck in gallons (y) is y=−10x+200y = -10x +200y=−10x+200.

STEP 6

To graph this function, we start by plotting the y-intercept (0,200) on the graph.

STEP 7

Then, we use the slope to find other points on the graph. Since the slope is -10, this means that for every increase of1 hour in driving time, the amount of fuel decreases by10 gallons.

STEP 8

We can use the table given in the problem to find more points on the graph. For example, after5 hours of driving, there are150 gallons of fuel remaining. So, we plot the point (5,150) on the graph.

STEP 9

Similarly, we plot the points (,100) and (15,50) on the graph.

STEP 10

Finally, we draw a line through the points we have plotted. This line represents the linear function y=−10x+200y = -10x +200y=−10x+200.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionGraph the linear function for Tim's truck fuel: $y = 200 - 10x$ , where $x$ is time in hours and $y$ is fuel in gallons.

Assumptions1. The truck starts with a full tank containing200 gallons of fuel. . For every hour Tim drives, the truck consumes10 gallons of fuel.
3. The relationship between the time driven and the remaining fuel is linear.

We can represent the relationship between the time driven and the remaining fuel as a linear function. The general form of a linear function is $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept.

In our case, the slope $m$ is the rate of fuel consumption, which is -10 gallons per hour. The negative sign indicates that the amount of fuel decreases as time increases.

The y-intercept $c$ is the initial amount of fuel, which is200 gallons.

So, the linear function representing the relationship between the time driven in hours (x) and the fuel remaining in the truck in gallons (y) is $y = -10x +200$ .

Finally, we draw a line through the points we have plotted. This line represents the linear function $y = -10x +200$ .