Question

Which graph represents the proportional relationship given by the rule "y is 3 times the value of x"?

Answer 1

Answer:

It's the bottom right graph.

Step-by-step explanation:

Answer 2

Answer:

The fourth graph i.e. RIGHT BOTTOM GRAPH is correct which represents the proportional relationship given by the rule y = 3x.

Also, the correct graph is attached below.

Step-by-step explanation:

Given the rule

''y is 3 times the value of x".

It means

y = 3x

comparing with the slope-intercept form of the line equation

y = mx+b

where y is the slope and b is the intercept

so,

The slope of y = 3x will be: m = 3

The y-intercept of  y = 3x will be: b = 0

CHECKING THE 4TH GRAPH (THE RIGHT BOTTOM SIDE)

Taking two points

(0, 0)

(2, 6)

Finding the slope between (0, 0) and (2, 6)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

                =  [6 - 0] / [2 - 0]

                = 6 / 2

               = 3

Thus, the slope of the line = m = 3

We know that the value of y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = 0

Thus, the y-intercept b = 0

Now, substituting m = 3 and b = 0 in the slope-intercept form of linear function

y = mx+b

y = 3x+0

y = 3x

Therefore, the fourth graph i.e. RIGHT BOTTOM GRAPH is correct which represents the proportional relationship given by the rule y = 3x.

Also, the correct graph is attached below.