Respuesta :

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 = [tex]\frac{61-0}{2-0}[/tex] = [tex]\frac{61}{2}[/tex] = 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