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User Rhapsody
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Answer:


\begin{array} c \cline{1-2} x & y\\\cline{1-2} -3 & 0\\\cline{1-2} -2 & 1\\\cline{1-2} -1 & 2\\\cline{1-2} 0 & 3\\\cline{1-2} 1 & 4\\\cline{1-2} 2 & 5\\\cline{1-2}\end{array}

non-proportional

Explanation:

Given equation:


y=x+3

Create a table of ordered pairs using the given equation:


\begin{array} c \cline{1-3} x & x+3 & y\\\cline{1-3} -3 & -3+3 & 0\\\cline{1-3} -2 & -2+3 & 1\\\cline{1-3} -1 & -1+3 & 2\\\cline{1-3} 0 & 0+3 & 3\\\cline{1-3} 1 & 1+3 & 4\\\cline{1-3} 2 & 2+3 & 5\\\cline{1-3}\end{array} \implies \begin{array}\cline{1-2} x & y\\\cline{1-2} -3 & 0\\\cline{1-2} -2 & 1\\\cline{1-2} -1 & 2\\\cline{1-2} 0 & 3\\\cline{1-2} 1 & 4\\\cline{1-2} 2 & 5\\\cline{1-2}\end{array}

Graph

As the given equation is linear, plot two of the ordered pairs and draw a straight line through them. (See attachment).

Proportional Relationship

A relationship in which two quantities vary directly with each other.

y varies directly as x:


y=kx

(where k is some constant)

To find if the relationship is proportional using the table, find the ratio
(y)/(x) of each row. If the ratio is the same, the relationship is proportional.


\begin{array}\cline{1-3} x & y & (y)/(x)\\\cline{1-3} -3 & 0 & 0\\\cline{1-3} -2 & 1 & -0.5} \\\cline{1-3} -1 & 2 & -2 \\\cline{1-3} 0 & 3 & \text{-}\\\cline{1-3} 1 & 4 & 4\\\cline{1-3} 2 & 5 & 2.5\\\cline{1-3}\end{array}

Graphs of proportional relationships pass through the origin (0, 0).

Therefore, the relationship is non-proportional because:

  • The ratios of y/x of each row of the table are not the same.
  • The graph does not pass through the origin.
  • There is the addition of a constant in the given equation, which means that y does not vary directly as x.
Pleasee help 100 points-example-1
User Dikuw
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