Question

The manager of a weekend flea market knows from past experience that if she charges xdollars for a rental space at the flea market, then the number yof spaces she can rent is given by the equation $y=200-4x$.

(a)Sketch a graph of this linear equation. (Remember that the rental charge per space and the number of spaces rented must both be non-negative quantities.)

(b)What do the slope, the y-intercept, and the x-intercept of the graph represent?

Short answer

(a) The answer is the graph of$y=200-4x.$

(b) The slope of the line is $-4$and intercept is 200.

Step-by-step solution

Part a. Step 1. Concept of Slope-Intercept form of the equation of the line.

Suppose a non-vertical line has a slope m and y-intercept b. This means that the line intersects the y-axis at the point $\left(0,b\right),$so the point slope form of the equation of the line with $x=0$and $y=b$becomes

$\begin{array}{c}(y-b)=m(x-0)\\ y=mx+b\end{array}$

This equation is called as the Slope-Intercept form of the Equation of the Line.

Part a. Step 2. Concept of graph.

Graph is a mathematical representation of a network which describes the relationship between lines and points.The graph of linear equation in two variables is a line.

Part a. Step 3. Sketching the graph.

The given equation is

$y=200-4x$

The graph of equation is as follows,

Part b. Step 1. Concept of Slope-Intercept form of the equation of the line.

Suppose a non-vertical line has a slope m and y-intercept b. This means that the line intersects the y-axis at the point $\left(0,b\right),$so the point slope form of the equation of the line with $x=0$and $y=b$becomes

$\begin{array}{c}(y-b)=m(x-0)\\ y=mx+b\end{array}$

This equation is called as the Slope-Intercept form of the Equation of the Line.

Part b. Step 2. Concept of y-intercept.

The y-coordinate is a point where a line curve or a surface intersects the y-axis.

Part b. Step 3. Determining the slope and y-intercept.

The given equation is

$y=200-4x$

Hence, the slope of the line is $-4$and y-intercept is 200.