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
[tex]y=16x[/tex]
If [tex]x=10,[/tex] then [tex]y=16\cdot 10=160[/tex] 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
[tex]y=0.45x[/tex]
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
[tex]y=12.5x[/tex]
When [tex]x=14,[/tex] then [tex]y=12.5\cdot 14=175[/tex]
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 [tex]40\div 5=8[/tex]
and for x = 700, y must be [tex]7\cdot 8=56[/tex] 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 [tex]k=1.75[/tex]
The equation of proportionality is [tex]y=1.75x[/tex]
When [tex]y=28,[/tex] then
[tex]28=1.75x\\ \\x=\dfrac{28}{1.75}\\ \\x=16[/tex]
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
[tex]k=\dfrac{61}{2}=30.5[/tex]
The equation of proportional relationship is
[tex]y=30.5x[/tex]
When [tex]y=274.50,[/tex] then
[tex]274.50=30.5x\\ \\x=\dfrac{274.5}{30.5}\\ \\x=9[/tex]
This means you could buy 9 tickets for $274.50
Q7. The equation which represent proportional relationship should have the equation of the form
[tex]y=kx[/tex]
Circle all equations in this form:
[tex]y=5x\\ \\p=0.5m\\ \\y=\dfrac{1}{2}x\\ \\M=3n\\ \\y=2x[/tex]
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.
