Question

write equations from tables and graphs

1. the graph shows the total sales of tickets to a school performance.

a. write an equation that relates the total sales to the number of tickets sold. use t for the total sales and n for the number of tickets.
b. if the number of tickets sold is 125, what will be the total sales?

1. stem the table shows the relationship between the mass m and the force w of weights on the ground. write an equation representing this relationship.

force (newtons) 9.8 19.6 29.4 39.2
mass (kilograms) 1 2 3 4
model with mathematics for problems 3–6, write an equation representing each graph or table.

1. graph of a line through the origin with points plotted
2. graph of a line with y - intercept 6
3. table with x: 0, 3, 6, 9, 12, 15 and y: 11.2, 14.2, 17.2, 20.2, 23.2, 26.2
4. table with x: 0, 2, 4, 6, 8, 10 and y: 0, 17, 34, 51, 68, 85

Explanation:

Problem 1A

Step1: Determine the slope (rate of change)

From the graph, when \( n = 0 \), \( T = 0 \); when \( n = 2 \), \( T = 8 \) (assuming the first non - zero point). The slope \( m=\frac{T_2 - T_1}{n_2 - n_1}=\frac{8 - 0}{2 - 0}=4 \).

Step2: Write the equation

Since it's a proportional relationship (passes through the origin), the equation is \( T = 4n \).

Step1: Use the equation from 1A

We have the equation \( T = 4n \), and \( n = 125 \).

Step2: Substitute \( n = 125 \) into the equation

\( T=4\times125 = 500 \).

Step1: Determine the slope (rate of change)

The slope \( m=\frac{w_2 - w_1}{m_2 - m_1}\). Taking \( m_1 = 1,w_1 = 9.8 \) and \( m_2 = 2,w_2 = 19.6 \), \( m=\frac{19.6 - 9.8}{2 - 1}=9.8 \).

Step2: Write the equation

Since it's a proportional relationship (when \( m = 0 \), \( w = 0 \)), the equation is \( w=9.8m \).

Answer:

\( T = 4n \)

Problem 1B