Question

A construction crew is lengthening a road. Let y represent the total length of the road (in miles). Let x represent the number of days the crew has worked. Suppose that x and y are related by the equation y=59+4x . Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.

What was the road's length when the crew started working? miles

What is the change per day in the road's length? miles

Answer 1

Based off of the equation, the road was 59 miles to start with. Because x represents the number of days working, and it is being multiplied by 4, the crew is changing the road by 4 miles a day.

Answer 2

The given expression is

`y=59+4x`

Where
`y` represent miles and
`x` represents days.

If we analyse this expression, we would find that the initial condition is 59 miles, which means that when the started to work, the road was 59 miles long.

The second term of the expression
`4x` expresses the ratio of change of the linear relation, which means that they work 4 miles per day.

Based on this analysis, we can answer all given questions.

• When they started to work, the road's length was 59 miles, because that's the initial condition of the linear relation.
• The change per day refers to the rate of change between variables, which is the coefficient of
  `x`. Therefore, the change per day in the road's length is 4 miles per day.