Answer:
[tex]\begin{array}{| c | 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}[/tex]
non-proportional
Step-by-step explanation:
Given equation:
[tex]y=x+3[/tex]
Create a table of ordered pairs using the given equation:
[tex]\begin{array}{| c | c | 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}{| c | 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}[/tex]
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:
[tex]y=kx[/tex]
(where k is some constant)
To find if the relationship is proportional using the table, find the ratio [tex]\dfrac{y}{x}[/tex] of each row. If the ratio is the same, the relationship is proportional.
[tex]\begin{array}{| c | c | c |}\cline{1-3} x & y & \dfrac{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}[/tex]
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.
