Question

10 the table below shows the costs of buying concert tickets online.
cost of tickets
number of tickets | 1 | 2 | 3 | 4
cost ($) | $30 | $50 | $70 | $90
part a
graph a line that represents the relationship shown in the table.
graph grid with y - axis cost ($) from 0 - 100, x - axis number of tickets 0 - 5
part b
does the graph show a proportional relationship?
circle the correct answers to complete the sentences.
the line does / does not pass through all four points and the origin.
therefore, the relationship in the graph is / is not a proportional relationship.

Explanation:

Part A

Step1: Identify Coordinates

From the table, the points are \((1, 30)\), \((2, 50)\), \((3, 70)\), \((4, 90)\).

Step2: Plot Points

On the graph, mark the points: for \(x = 1\), \(y = 30\); \(x = 2\), \(y = 50\); \(x = 3\), \(y = 70\); \(x = 4\), \(y = 90\). Then draw a straight line through these points.

Part B

Step1: Check Origin

A proportional relationship has a graph that passes through the origin \((0,0)\). Let's see if the line passes through \((0,0)\). For \(x = 0\), using the pattern (slope \(m=\frac{50 - 30}{2 - 1}=20\), equation \(y - 30 = 20(x - 1)\) → \(y = 20x + 10\)). At \(x = 0\), \(y = 10
eq0\), so the line does not pass through the origin. Also, check if the line passes through all four points: the points \((1,30)\), \((2,50)\), \((3,70)\), \((4,90)\) lie on the line \(y = 20x + 10\) (e.g., \(x = 1\), \(y = 20(1)+10 = 30\); \(x = 2\), \(y = 20(2)+10 = 50\), etc.), but not the origin.

Step2: Determine Proportionality

A proportional relationship requires the graph to be a straight line through the origin. Since this line does not pass through the origin, the relationship is not proportional.

Answer:

(Part A):
(Graph with points \((1, 30)\), \((2, 50)\), \((3, 70)\), \((4, 90)\) plotted and a line drawn through them)