Question

SOS! PLEASE HELP ME!!

Answer 1

Answer:

a) The point (4, 122) represents that the cost of 4 tickets is $122

b) The unit rate is 30.5 dollars per ticket

c) The cost of buying 10 tickets is $305

Step-by-step explanation:

Let us solve the question

From the given graph

∵ The x-axis represents the number of tickets

∵ The y-axis represents the cost of tickets in dollars

∴ The line represents the relationship between the number of tickets

   and their cost

a)

∵ The point (4, 122) lies on the line

∴ x = the number of tickets

∴ y = their cost

∵ x = 4 and y = 122

∴ The cost of the 4 tickets is 122 dollars

∴ The point (4, 122) represents that the cost of 4 tickets is $122

b)

∵ The unit rate is the slope of the line

∵ The slope of the line = Δy/Δx, where

• Δy = y2 - y1
• Δx = x2 - x1

∵ The line passes through points (0, 0) and (2, 61)

∴ x1 = 0 and x2 = 2

∴ y1 = 0 and y2 = 61

→ Substitute them in the rule of the slope above

∴ The slope of the line = $\frac{61-0}{2-0}$ = $\frac{61}{2}$ = 30.5

∴ The unit rate is 30.5 dollars per ticket

c)

∵ The linear equation is y = m x + b, where

• m is the slope of the line
• b is the y-intercept (value y at x = 0)

∵ m = 30.5 ⇒ the slope of the lone

∵ b = 0 ⇒ The line passes through the origin point (0, 0)

∴ The equation of the line is y = 30.5x

∵ x = 10 ⇒ number of tickets

→ Substitute x by 10 in the equation to find the cost of 10 tickets

∴ y = 30.5(10)

∴ y = 305

∴ The cost of buying 10 tickets is $305