Question

guided practice activity #4 - y - intercepts
this worksheet asks you to interpret y - intercepts.

1. monthly cell phone bill:

cost of 5c plan with the monthly fee
a. interpret y - intercept of the equation in real world terms.

1. concentration of pollutants:

a. interpret the y - intercept of the equation in real world terms.

Explanation:

1a. Interpreting the y - intercept for the cell phone bill equation

Step 1: Recall the slope - intercept form

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. For the equation $y=0.05x + 20$, the y - intercept $b = 20$.

Step 2: Analyze the variables

In the context of the cell phone bill, $x$ represents the number of minutes used and $y$ represents the total cost of the cell phone bill (in dollars). When $x = 0$ (which means 0 minutes of call time are used), we substitute $x = 0$ into the equation: $y=0.05(0)+20=20$.

Step 1: Recall the slope - intercept form

The equation of the line is $y=- 0.8x + 100$, where $x$ is the number of days and $y$ is the concentration of pollutants (in ppm). The y - intercept $b = 100$.

Step 2: Analyze the variables

When $x = 0$ (which means at day 0, or the start of the observation period), we substitute $x = 0$ into the equation: $y=-0.8(0)+100 = 100$.

Answer:

When the number of minutes of call time used ($x$) is 0, the total monthly cell phone bill ($y$) is $20. This means that there is a fixed monthly fee of $20 for the cell phone plan, even if no minutes are used.

2a. Interpreting the y - intercept for the pollutant concentration equation