Question

a park ranger is planting trees in the picnic area. the graph shows the number of trees left to plant. the equation for the number of trees left to plant is $y = -7x + 35$. select the meaning of the slope and $y$-intercept from the drop-down menus. in the scenario, the slope represents in the scenario, the $y$-intercept represents

Explanation:

Step1: Recall the slope - intercept form

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(y=-7x + 35\), \(m=-7\) and \(b = 35\).

Step2: Interpret the slope

The slope \(m=-7=\frac{\text{Change in }y}{\text{Change in }x}\). Here, \(y\) represents the number of trees left to plant and \(x\) represents the number of days. A slope of \(- 7\) means that for each increase of 1 in the number of days (\(x\)), the number of trees left to plant (\(y\)) decreases by 7. So the slope represents the number of trees planted per day.

Step3: Interpret the \(y\) - intercept

The \(y\) - intercept occurs when \(x = 0\). When \(x = 0\) (at the start, i.e., day 0), \(y=-7\times0+35=35\). So the \(y\) - intercept represents the initial number of trees to plant.

Answer:

In the scenario, the slope represents the number of trees planted per day. In the scenario, the \(y\) - intercept represents the initial number of trees to plant.