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.
