lolokn13
contestada

A linear function m models the amount of milk sold by a farm per month. The amount decreases 500 gallons for every $1 increase in price. Graph m when m(0)=3000. Identify the slope. Interpret the x- and y-intercepts of the graph.

Respuesta :

Limosa

Answer:

Slope of the graph [tex]-500[/tex] gallons per dollar.

Intercept is 3000.

Step-by-step explanation:

General format of an equation of a linear graph is;

y=mx+c

Where,

y is the dependent variable

m is the slope of the graph

x is the independent variable of the graph

c is the intercept of the graph.

m(0)=3000 means when we substitute 0 for x values of the graph the y value is 3000. Therefore the intercept is 3000.

Slope of the graph = [tex]\frac{-500gallons}{1dollar}[/tex]

                               =[tex]-500[/tex] gallons per dollar.

So we can write the equation as;

[tex]y=-500x+3000[/tex]

but in this question y is given as m. Therefore function can be re-written as:

[tex]m=-500x+3000[/tex]

The graph is attached with the answer.



Ver imagen Limosa
Ver imagen Limosa

The linear function that models this situation is:

[tex]m(x) = 3000 - 500x, 0 \leq x \leq 6[/tex]

  • The y-intercept is y = 3000, which means that when there is no increase on the price, the farm sells 3000 gallons.
  • The x-intercept is x = 6, which means that if the price increases $6, no gallons will be sold.
  • The slope is of -500.
  • The graph is sketched at the end of this answer.

The equation of a line has the following format:

[tex]y = ax + b[/tex]

In which:

  • a is the slope, which is by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0.

In this problem, m(0) = 3000, thus, [tex]b = 3000[/tex], that is:

  • The y-intercept is y = 3000, which means that when there is no increase on the price, the farm sells 3000 gallons.

The amount decreases 500 gallons for every $1 increase in price, thus, the slope is -500, and the equation is:

[tex]m(x) = 3000 - 500x[/tex]

The x-intercept is the value of x for which:

[tex]m(x) = 0[/tex]

Then

[tex]500x = 3000[/tex]

[tex]x = \frac{3000}{500}[/tex]

[tex]x = 6[/tex]

  • The x-intercept is x = 6, which means that if the price increases $6, no gallons will be sold.

A similar problem is given at https://brainly.com/question/24808124

Ver imagen joaobezerra

Otras preguntas