**Analyzing graph worksheet :**

Worksheet on analyzing graph is much useful to the students who would like to practice problems on solving real-world problems using graphs.

Many real-world situations can be represented by linear relationships. We can use graphs of linear relationships to visualize situations and solve problems.

Recall that y = mx + b is the slope-intercept form of the equation of a line.

In this form, it is easy to see the slope "m" and the y-intercept "b". So we can use this form to quickly graph a line by plotting the point (0, b) and using the slope to find a second point.

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 ?

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.

**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).

**Store A**

200 = 20x + 60

140 = 20x

7 = x

**Store B**

200 = 10x + 100

100 = 10x

10 = x

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

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

After having gone through the stuff given above, we hope that the students would have understood, "Analyzing graph worksheet".

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