Answer :
To write the equation representing the relationship between the number of days and the total charges for placing a classified ad, we will use the given data points and derive the equation in slope-intercept form [tex]\( y = mx + b \)[/tex].
### Step-by-Step Solution:
1. Identify the Data Points:
The given data points are:
[tex]\[ (2, 8), (4, 13), (6, 18) \][/tex]
2. Calculate the Slope (m):
To find the slope ([tex]\(m\)[/tex]), we use two of the given data points. Let's use the points [tex]\((2, 8)\)[/tex] and [tex]\((4, 13)\)[/tex]:
[tex]\[ \text{Slope} (m) = \frac{\Delta y}{\Delta x} = \frac{13 - 8}{4 - 2} = \frac{5}{2} = 2.5 \][/tex]
3. Determine the Intercept (b):
Using the slope and one of the points (let's use [tex]\((2, 8)\)[/tex]), we can find the y-intercept ([tex]\(b\)[/tex]) by plugging the values into the slope-intercept form equation [tex]\( y = mx + b \)[/tex]:
[tex]\[ 8 = 2.5 \cdot 2 + b \][/tex]
Solving for [tex]\(b\)[/tex]:
[tex]\[ 8 = 5 + b \\ b = 8 - 5 \\ b = 3 \][/tex]
4. Formulate the Equation:
With the slope [tex]\(m = 2.5\)[/tex] and the y-intercept [tex]\(b = 3\)[/tex], the equation in slope-intercept form is:
[tex]\[ y = 2.5x + 3 \][/tex]
### Conclusion:
The equation representing the relationship between the number of days (x) and the total charges (y) for placing a classified ad is:
[tex]\[ y = 2.5x + 3 \][/tex]
This equation implies that the newspaper charges a flat fee of [tex]$3.00, plus an additional $[/tex]2.50 per day for the ad.
### Step-by-Step Solution:
1. Identify the Data Points:
The given data points are:
[tex]\[ (2, 8), (4, 13), (6, 18) \][/tex]
2. Calculate the Slope (m):
To find the slope ([tex]\(m\)[/tex]), we use two of the given data points. Let's use the points [tex]\((2, 8)\)[/tex] and [tex]\((4, 13)\)[/tex]:
[tex]\[ \text{Slope} (m) = \frac{\Delta y}{\Delta x} = \frac{13 - 8}{4 - 2} = \frac{5}{2} = 2.5 \][/tex]
3. Determine the Intercept (b):
Using the slope and one of the points (let's use [tex]\((2, 8)\)[/tex]), we can find the y-intercept ([tex]\(b\)[/tex]) by plugging the values into the slope-intercept form equation [tex]\( y = mx + b \)[/tex]:
[tex]\[ 8 = 2.5 \cdot 2 + b \][/tex]
Solving for [tex]\(b\)[/tex]:
[tex]\[ 8 = 5 + b \\ b = 8 - 5 \\ b = 3 \][/tex]
4. Formulate the Equation:
With the slope [tex]\(m = 2.5\)[/tex] and the y-intercept [tex]\(b = 3\)[/tex], the equation in slope-intercept form is:
[tex]\[ y = 2.5x + 3 \][/tex]
### Conclusion:
The equation representing the relationship between the number of days (x) and the total charges (y) for placing a classified ad is:
[tex]\[ y = 2.5x + 3 \][/tex]
This equation implies that the newspaper charges a flat fee of [tex]$3.00, plus an additional $[/tex]2.50 per day for the ad.
