Question

a city has 4 inches of rain for the year. a storm then hits the city, adding an inch of rain to the citys yearly total each day. write the linear function that finds the total inches of rainfall, y, based on the total days since the storm hit, x. additionally, find the y-intercept of that function.
y =
y-intercept :

Explanation:

Step1: Identify the slope and initial value

The storm adds 1 inch of rain each day, so the slope \( m = 1 \). Before the storm (when \( x = 0 \)), the city already had 4 inches of rain, so the initial value (y-intercept) is 4.

Step2: Write the linear function

The slope - intercept form of a linear function is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Substituting \( m = 1 \) and \( b = 4 \), we get \( y=x + 4 \).

Step3: Find the y - intercept

The y - intercept of a linear function \( y=mx + b \) is the value of \( y \) when \( x = 0 \). From the function \( y=x + 4 \), when \( x = 0 \), \( y=4 \). So the y - intercept is 4.

Answer:

The linear function is \( y=x + 4 \) and the y - intercept is 4.