ANALYZING GRAPH WORKSHEET

Problem 1 :

Ken has a weekly goal of burning 2400 calories by taking brisk walks. The equation y = -300x + 2400 represents the number of calories y Ken has left to burn after x hours of walking which burns 300 calories per hour.After how many hours of walking will Ken have 600 calories left to burn ? After how many hours will he reach his weekly goal ?

Problem 2 :

Jose wants to buy a new game system that costs $200. He does not have enough money to buy it today, so he compares layaway plans at different stores. Store A requires an initial payment of $60 and weekly payments of $20 until the balance is paid in full. The plan at Store B is shown on the graph.

Based on the information given above, find which store allows Jose to pay for the game system faster. 

Detailed Answer Key

Problem 1 :

Ken has a weekly goal of burning 2400 calories by taking brisk walks. The equation y = -300x + 2400 represents the number of calories y Ken has left to burn after x hours of walking which burns 300 calories per hour.After how many hours of walking will Ken have 600 calories left to burn ? After how many hours will he reach his weekly goal ?

Solution : 

Step 1 :

 y = -300x + 2400

The y-intercept is b = 2400. Plot the point that contains the y-intercept : (0, 2400).

Step 2 : 

Write the slope as a fraction.

m  =  -300/1  =  -600/2  =  -900/3

Using the slope as -900/3 helps in drawing a more accurate graph.

The slope is m = -900/3. Use the slope to find second a point. Since the slope  =  rise / run, from (0, 2400), count down 900 units and right 3 units. 

Then, the new point is (3, 1500). 

Step 3 : 

Draw a line through the points. 

Step 4 : 

To find after how many hours of walking will Ken have 600 calories left to burn, 

Locate 600 calories on the y-axis. Read across and down to the x-axis.

From the graph, we can know that Ken will have 600 calories left to burn after 6 hours.

Step 5 : 

Ken will reach his weekly goal when the number of calories left to burn is 0. Because every point on the x-axis has a y-value of 0, find the point where the line crosses the x-axis.

Ken will reach his goal after 8 hours of brisk walking.

Problem 2 :

Jose wants to buy a new game system that costs $200. He does not have enough money to buy it today, so he compares layaway plans at different stores. Store A requires an initial payment of $60 and weekly payments of $20 until the balance is paid in full. The plan at Store B is shown on the graph.

Based on the information given above, find which store allows Jose to pay for the game system faster. 

Solution : 

Step 1 :

To find which store allows Jose to pay for the game system faster, let us have the deals offered by store A and B as equations.

Write an equation in slope-intercept form for Store A’s layaway plan.

Let x represent number of weeks and y represent the total money to be paid.

y  =  20x + 60

Step 2 :

Write an equation in slope-intercept form for Store B’s layaway plan.

Let x represent number of weeks and y represent the total money to be paid. 

From the graph, y - intercept is 100 and the slope is 10

y  =  10x + 100

Step 3 :

In both the stores A and B, find the value of "x" (no. of weeks) for y = $200 (Total money to be paid). 

The total amount $200 is completed in 7 weeks in store A and in 10 weeks in store B. 

So, store A allows Jose to pay for the game system faster.

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