Which graph represents the proportional relationship given by the rule "y is 3 times the value of x"?
2 answers:
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.
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Arc XZ is marked in red (see the image attachment)
Angle XYZ is marked in blue
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measure of arc XZ = 28 degrees
measure of angle XYZ = (1/2)*(measure of arc XZ)
measure of angle XYZ = (1/2)*(28 degrees)
measure of angle XYZ = 14 degrees
Answer: D) 14 degrees
Angle XYZ is marked in blue
It turns out that angle XYZ is exactly half the measure of arc XZ. This is due to the inscribed angle theorem. Angle XYZ is an inscribed angle that cuts off, or subtends, arc XZ.
measure of arc XZ = 28 degrees
measure of angle XYZ = (1/2)*(measure of arc XZ)
measure of angle XYZ = (1/2)*(28 degrees)
measure of angle XYZ = 14 degrees
Answer: D) 14 degrees