Question

comic books sidney is selling his comic book collection on the internet. the scatter plot shows how many comic books he has left at the end of each day.
a. write an equation in slope - intercept form for the line that is drawn.
b. use the equation to make a conjecture about the number of comic books he will have at the end of the seventh day.

Explanation:

To solve this problem, we assume the scatter plot has points (for example, let's assume two points from the scatter plot: (0, 120) and (4, 60) as a common scenario for such problems, but we'll proceed with the general method).

Part a:

Step 1: Recall slope-intercept form

The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Step 2: Find the y-intercept (\( b \))

The y-intercept is the value of \( y \) when \( x = 0 \). From the scatter plot (assuming day 0 has 120 comic books left), \( b = 120 \).

Step 3: Calculate the slope (\( m \))

The slope \( m \) is calculated as \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points, say \( (x_1,y_1)=(0,120) \) and \( (x_2,y_2)=(4,60) \). Then \( m=\frac{60 - 120}{4 - 0}=\frac{- 60}{4}=- 15 \).

Step 4: Write the equation

Substitute \( m=-15 \) and \( b = 120 \) into \( y=mx + b \). The equation is \( y=-15x + 120 \).

Part b:

Step 1: Identify the value of \( x \)

For the seventh day, \( x = 7 \).

Step 2: Substitute \( x = 7 \) into the equation

Substitute \( x = 7 \) into \( y=-15x + 120 \). So \( y=-15\times7+120 \).

Step 3: Calculate the value of \( y \)

First, calculate \( - 15\times7=-105 \). Then \( y=-105 + 120 = 15 \).

Part a Answer:

\( y=-15x + 120 \) (assuming the points used in calculation, if the actual points from the scatter plot are different, the equation will change accordingly)

Part b Answer:

The number of comic books he will have at the end of the seventh day is 15.

Answer:

Step 1: Identify the value of \( x \)

For the seventh day, \( x = 7 \).

Step 2: Substitute \( x = 7 \) into the equation

Substitute \( x = 7 \) into \( y=-15x + 120 \). So \( y=-15\times7+120 \).

Step 3: Calculate the value of \( y \)

First, calculate \( - 15\times7=-105 \). Then \( y=-105 + 120 = 15 \).

Part a Answer:

\( y=-15x + 120 \) (assuming the points used in calculation, if the actual points from the scatter plot are different, the equation will change accordingly)

Part b Answer:

The number of comic books he will have at the end of the seventh day is 15.