Answer :
Certainly! Let's walk through how to build the equation of the line based on the problem statement step-by-step.
### Step-by-Step Solution
1. Understand the Problem:
Myra charges a flat rate of [tex]$5 regardless of the miles driven. Additionally, she charges $[/tex]0.50 (50 cents) per mile driven.
2. Identify Given Information:
- The charge starts at [tex]$5, which means when no miles are driven (x = 0), the cost is $[/tex]5.
- The cost increases by [tex]$0.50 for each mile driven. 3. Determine the \( y \)-intercept and Slope: The y-intercept occurs at \( x = 0 \), where \( y \) is 5. So, \( y \)-intercept \( (b) = 5 \). The slope (m) is the rate of change in cost with respect to miles driven, which is $[/tex]0.50 per mile. Thus, [tex]\( m = 0.5 \)[/tex].
4. Form the Equation:
Using the slope-intercept form of a line [tex]\( y = mx + b \)[/tex]:
- [tex]\( y \)[/tex] is the total cost.
- [tex]\( x \)[/tex] is the number of miles driven.
- [tex]\( m \)[/tex] is the slope (0.5).
- [tex]\( b \)[/tex] is the intercept (5).
Therefore, the equation can be written as:
[tex]\[ y = 0.5x + 5 \][/tex]
Therefore, the equation that represents Myra's car service charges is [tex]\( y = 0.5x + 5 \)[/tex]. This equation shows that for each additional mile driven ([tex]\( x \)[/tex]), the total cost ([tex]\( y \)[/tex]) increases by [tex]$0.50, starting from the $[/tex]5 flat rate.
### Step-by-Step Solution
1. Understand the Problem:
Myra charges a flat rate of [tex]$5 regardless of the miles driven. Additionally, she charges $[/tex]0.50 (50 cents) per mile driven.
2. Identify Given Information:
- The charge starts at [tex]$5, which means when no miles are driven (x = 0), the cost is $[/tex]5.
- The cost increases by [tex]$0.50 for each mile driven. 3. Determine the \( y \)-intercept and Slope: The y-intercept occurs at \( x = 0 \), where \( y \) is 5. So, \( y \)-intercept \( (b) = 5 \). The slope (m) is the rate of change in cost with respect to miles driven, which is $[/tex]0.50 per mile. Thus, [tex]\( m = 0.5 \)[/tex].
4. Form the Equation:
Using the slope-intercept form of a line [tex]\( y = mx + b \)[/tex]:
- [tex]\( y \)[/tex] is the total cost.
- [tex]\( x \)[/tex] is the number of miles driven.
- [tex]\( m \)[/tex] is the slope (0.5).
- [tex]\( b \)[/tex] is the intercept (5).
Therefore, the equation can be written as:
[tex]\[ y = 0.5x + 5 \][/tex]
Therefore, the equation that represents Myra's car service charges is [tex]\( y = 0.5x + 5 \)[/tex]. This equation shows that for each additional mile driven ([tex]\( x \)[/tex]), the total cost ([tex]\( y \)[/tex]) increases by [tex]$0.50, starting from the $[/tex]5 flat rate.
