contestada

A proportional relationship is shown in the table below:
xxx 000 111 222 333 444
yyy 000 333 666 999 121212
What is the slope of the line that represents this relationship?
\qquadspace

Graph the line that represents this relationship.

Respuesta :

calculista

Answer:

The slope is [tex]m=3[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

[tex]A(1,3)[/tex] ------> from the given table

Find the value of k

[tex]k=y/x[/tex]

substitute the values

[tex]k=3/1=3[/tex]

The linear equation is

[tex]y=3x[/tex]

using a graphing tool

see the attached figure

Ver imagen calculista
MrRoyal

The slope of a proportional relationship is the rate of change of the relationship

The slope of the relationship is 3

Pick any two points from the table;

[tex]\mathbf{(x,y) = (0,0) (1,3)}[/tex]

The slope (m) is calculated as:

[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

So, we have:

[tex]\mathbf{m = \frac{3 - 0}{1 - 0}}[/tex]

Subtract

[tex]\mathbf{m = \frac{3}{1}}[/tex]

Divide

[tex]\mathbf{m = 3}[/tex]

Hence, the slope of the relationship is 3

Because it is a proportional relationship, the equation of its graph is:

[tex]\mathbf{y = mx}[/tex]

Substitute 3 for m

[tex]\mathbf{y = 3x}[/tex]

See attachment for the graph of [tex]\mathbf{y = 3x}[/tex]

Read more about proportional relationships at:

https://brainly.com/question/24312388

Ver imagen MrRoyal
Q&A Education