Question

1. danny is opening a savings account with an initial deposit of $45. he saves $3 per day.

a. draw a line to show the relationship between the number of days, x, and the total amount in his account, y.
b. what is the equation of the line in slope - intercept form?

Explanation:

Part a

Step1: Identify the y-intercept

The initial deposit is $45, so when \( x = 0 \) (0 days), \( y = 45 \). This is the y-intercept \((0, 45)\).

Step2: Identify the slope

He saves $3 per day, so the slope \( m = 3 \) (rate of change of y with respect to x).

Step3: Plot points and draw the line

• Start at the y-intercept \((0, 45)\).
• For each increase of 1 in \( x \) (1 day), increase \( y \) by 3 (since slope is 3). So, when \( x = 1 \), \( y = 45 + 3 = 48 \); when \( x = 2 \), \( y = 45 + 6 = 51 \), and so on.
• Use these points to draw a straight line on the given graph.

Part b

Step1: 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.

Step2: Determine \( m \) and \( b \)

• The slope \( m \): Danny saves $3 per day, so the rate of change of the amount in his account with respect to the number of days is 3. Thus, \( m = 3 \).
• The y - intercept \( b \): The initial deposit is $45, which is the amount in the account when the number of days \( x = 0 \). So, \( b = 45 \).

Step3: Write the equation

Substitute \( m = 3 \) and \( b = 45 \) into the slope - intercept form \( y=mx + b \). We get \( y = 3x+45 \).

Answer:

(Part a):
Draw a line starting at the point \((0, 45)\) on the y - axis and with a slope of 3 (going up 3 units for every 1 unit to the right on the x - axis).