Question

Which equations have a greater unit rate than the rate represented in the table? x y 3 2 6 4 9 6

Answer 1

Slope of table

• (3,2)
• (6,4)

Slope

• m=4-2/6-3
• m=2/3

Any equation having slope greater than 2/3 has higher unit rate than that of table

Answer 2

Any equation with a slope greater than ²/₃

Explanation:

Given table:

`\begin{array}\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}`

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

`y = mx + b`

where:

• m is the slope
• b is the y-intercept

To find the slope, take two ordered pairs from the table:

`\sf let \: (x_1,y_1)=(3,2)`

`\sf let \: (x_2,y_2)=(6,4)`

Substitute them into the slope equation:

`\sf slope=(y_2-y_1)/(x_2-x_1)=(4-2)/(6-3)=(2)/(3)`

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.