Answer:
Any equation with a slope greater than ²/₃
Step-by-step explanation:
Given table:
[tex]\begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 3 & 2 \\\cline{1-2} 6 & 4 \\\cline{1-2} 9 & 6 \\\cline{1-2} \end{array}[/tex]
The unit rate is a ratio that compares the first quantity to one unit of the second quantity. The unit rate is also the slope of a linear equation.
Linear equation
[tex]y = mx + b[/tex]
where:
To find the slope, take two ordered pairs from the table:
[tex]\sf let \: (x_1,y_1)=(3,2)[/tex]
[tex]\sf let \: (x_2,y_2)=(6,4)[/tex]
Substitute them into the slope equation:
[tex]\sf slope=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-2}{6-3}=\dfrac{2}{3}[/tex]
Therefore, the unit rate is ²/₃.
Any equation with a slope greater than ²/₃ is an equation with a greater unit rate than that represented in the given table.
Slope of table
Slope
Any equation having slope greater than 2/3 has higher unit rate than that of table
