Please help 100 points and brainlest for all the answers

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.

entering that problem on the tube might get you an answer