Question

jack starts with 2 dollars in his account. he deposits the same amount of money each day. this graph represents the relationship between the number of days and the amount in the bank account. use the slope and vertical intercept to write an equation. slope =

Explanation:

Step1: Identify two points

From the graph, when \( x = 0 \), \( d = 2 \) (the y - intercept). Another point: when \( x = 1 \), \( d = 10 \) (by looking at the graph, at \( x = 1 \), the value of \( d \) is 10).

Step2: Calculate the slope

The formula for slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let \( (x_1,y_1)=(0,2) \) and \( (x_2,y_2)=(1,10) \). Then \( m=\frac{10 - 2}{1 - 0}=\frac{8}{1}=8 \).

Step3: Write the equation

The slope - intercept form of a line is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( d \) (the amount in the account) is the dependent variable, \( x \) (the number of days) is the independent variable, \( m = 8 \) and \( b = 2 \). So the equation is \( d=8x + 2 \). Also, the slope is 8.

Answer:

Slope: \( 8 \)
Equation: \( d = 8x+2 \)