Answer:
See explanation
Step-by-step explanation:
Q1. The graph of given data is attached.
The relationship is directly proportional as the line connecting all points is straight line passing through the origin.
For every 1 unit change in x, the change of y is 16.
Therefore, the equation that represents this line is
If then
square feet.
Q2. Yes, the relationship shows the direct proportionality as the line connecting all points is straight line passing through the origin (see second attached graph).
For every 1 unit change in x, the change of y is 0.45.
Therefore, the equation of the line is
Q3. Yes, the relationship shows the direct proportionality as the line connecting all points is straight line passing through the origin.
Find the constant of proportionality:
If x = 2, y = 25, then
when x = 1, y = 12.5
so k = 12.5
and the equation of the line is
When then
Hence, the cost of 14 tickets is $175
Q4. This table does not show the direct variation because
if x = 500 and y = 40, then
for x = 100, y is
and for x = 700, y must be not 50.
Hence, this relationship does not show the direct proportionality between x and y.
Q5. This elationship shows the direct proportionality as the line connecting all points is straight line passing through the origin.
The constant of proportionality is
The equation of proportionality is
When then
This means for $28 you could buy 16 ice cream scoops.
Q6. The line passes through the point (2,61), so the constant of proportionality is
The equation of proportional relationship is
When then
This means you could buy 9 tickets for $274.50
Q7. The equation which represent proportional relationship should have the equation of the form
Circle all equations in this form:
Q8. A relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first. If y is directly proportional to x, the equation is of the form y = kx (where k is a constant).
This means that the graph of direct variation is always a straight line passing through the origin (because x = 0 and y = 0 satisfy the equation for all k).
Not all lines represent the proportional relationship. Only those, which pass through the origin.