Alg. 1: Direct Variation

The given statement states that when x = 2, y = 15 and when x = 8, y = 10. This implies that as x increases, y decreases. However, the statement "True" suggests that as x increases, y also increases, which contradicts the given information. Therefore, the correct answer is "False".

The given question states that y is directly proportional to x. This means that as x increases, y also increases in a linear manner. The formula for this relationship is y = kx, where k is the constant of proportionality. In this case, we are given that y = 16 when x = 4. By substituting these values into the formula, we can solve for k. Therefore, the formula for the relation between y and x is y = 4x.

The equation y=5x represents a direct variation because it follows the form y=kx, where k is a constant. In this case, the constant is 5, which means that for every increase in x by 1, y will increase by 5. Therefore, when x=9, y can be found by substituting the value into the equation: y=5(9)=45.

The given information states that the amount of money raised at a charity fundraiser is directly proportional to the number of attendees. This means that as the number of attendees increases, the amount of money raised will also increase in proportion. The question provides the amount of money raised for five attendees, which is $100. To find out how much money will be raised for 60 attendees, we can set up a proportion: 5 attendees correspond to $100, so 60 attendees will correspond to x amount of money. Solving this proportion, we find that x = $1,200. Therefore, $1,200 will be raised for 60 attendees.

The equation y=4/3x represents a direct variation because it follows the form y=kx, where k is the constant of variation. In this case, the constant of variation is 4/3, which means that for every increase in x by 1, y will increase by 4/3. Therefore, if x=24, we can substitute it into the equation to find y.