Which equation represents the graphed line?
- A. y = -1/3x +3
- B. y = 3x - 7
- C. y = 3x + 7
- D. y = 1/3x + 1
Correct Answer & Rationale
Correct Answer: D
The equation y = 1/3x + 1 accurately represents the graphed line due to its positive slope of 1/3, indicating a gradual upward rise, consistent with the line’s direction. The y-intercept of 1 shows that the line crosses the y-axis at the point (0, 1), aligning perfectly with the graph. Option A, with a slope of -1/3, suggests a downward trend, which contradicts the graph’s upward slope. Option B has a much steeper slope of 3, leading to a different angle of rise. Option C also has a slope of 3 and a y-intercept of 7, which does not match the graph’s intercept. Thus, only D accurately reflects both the slope and intercept of the line shown.
The equation y = 1/3x + 1 accurately represents the graphed line due to its positive slope of 1/3, indicating a gradual upward rise, consistent with the line’s direction. The y-intercept of 1 shows that the line crosses the y-axis at the point (0, 1), aligning perfectly with the graph. Option A, with a slope of -1/3, suggests a downward trend, which contradicts the graph’s upward slope. Option B has a much steeper slope of 3, leading to a different angle of rise. Option C also has a slope of 3 and a y-intercept of 7, which does not match the graph’s intercept. Thus, only D accurately reflects both the slope and intercept of the line shown.
Other Related Questions
Lisa is decorating her office with two fully stocked aquariums. She saw an advertisement for Jorge's pet store in the newspaper. Jorge's store sells fish for aquariums. The table shows the fish Lisa buys from Jorge's pet store.
Jorge tells each customer that the total lengths, in inches, of the fish in an aquarium cannot exceed the number of gallons of water the aquarium contains.
The newspaper advertisement for Jorge's pet store has an illustration of a gold barb.
The illustration is not the same length as the actual gold barb. What was the scale factor used to create the illustration?
- A. 0.75
- B. 1.25
- C. 1.75
- D. 1.75
Correct Answer & Rationale
Correct Answer: B
To determine the scale factor used in the illustration of the gold barb, we compare the actual length of the fish to the length shown in the advertisement. A scale factor greater than 1 indicates that the illustration is larger than the actual fish, while a scale factor less than 1 means it is smaller. Option A (0.75) suggests the illustration is smaller, which contradicts the premise. Option C (1.75) and D (1.75) both imply a larger size, but only one option can be correct. The scale factor of 1.25 accurately represents a reasonable enlargement of the fish, aligning with common advertising practices. Thus, it correctly reflects the relationship between the illustration and the actual size of the gold barb.
To determine the scale factor used in the illustration of the gold barb, we compare the actual length of the fish to the length shown in the advertisement. A scale factor greater than 1 indicates that the illustration is larger than the actual fish, while a scale factor less than 1 means it is smaller. Option A (0.75) suggests the illustration is smaller, which contradicts the premise. Option C (1.75) and D (1.75) both imply a larger size, but only one option can be correct. The scale factor of 1.25 accurately represents a reasonable enlargement of the fish, aligning with common advertising practices. Thus, it correctly reflects the relationship between the illustration and the actual size of the gold barb.
On a number line, what is the distance, in units, between 16 and -25
Correct Answer & Rationale
Correct Answer: 41 units
To find the distance between two points on a number line, subtract the smaller number from the larger number. Here, the calculation is |16 - (-25)|, which simplifies to |16 + 25| = |41|. This results in a distance of 41 units. Other options may suggest incorrect calculations. For instance, an answer like 9 units might arise from simply adding the two numbers without considering their positions on the number line, leading to an inaccurate interpretation of distance. Similarly, options like 25 or 16 units misrepresent the actual distance by not accounting for both numbers' magnitudes relative to zero.
To find the distance between two points on a number line, subtract the smaller number from the larger number. Here, the calculation is |16 - (-25)|, which simplifies to |16 + 25| = |41|. This results in a distance of 41 units. Other options may suggest incorrect calculations. For instance, an answer like 9 units might arise from simply adding the two numbers without considering their positions on the number line, leading to an inaccurate interpretation of distance. Similarly, options like 25 or 16 units misrepresent the actual distance by not accounting for both numbers' magnitudes relative to zero.
Ricardo has two bank accounts. Each month, he will withdraw a certain amount of money from the first account and deposit a different amount of money into the second account. The inequality 8,000 – 200x ? 5,000 + 300x can be solved to find the number of months, x, for which the account has more money than the second account. What is the solution to this inequality?
- A. x ? 6
- B. x ? 30
- C. x ? 30
- D. x ? 6
Correct Answer & Rationale
Correct Answer: D
To solve the inequality \( 8,000 - 200x > 5,000 + 300x \), we first isolate \( x \). Rearranging gives \( 8,000 - 5,000 > 300x + 200x \), simplifying to \( 3,000 > 500x \). Dividing by 500 results in \( x < 6 \). Thus, the solution indicates that for \( x \) to ensure the first account has more money, it must be less than 6 months. Option A incorrectly states \( x \geq 6 \), which contradicts the solution. Options B and C mistakenly suggest \( x \geq 30 \), which is not relevant to the problem.
To solve the inequality \( 8,000 - 200x > 5,000 + 300x \), we first isolate \( x \). Rearranging gives \( 8,000 - 5,000 > 300x + 200x \), simplifying to \( 3,000 > 500x \). Dividing by 500 results in \( x < 6 \). Thus, the solution indicates that for \( x \) to ensure the first account has more money, it must be less than 6 months. Option A incorrectly states \( x \geq 6 \), which contradicts the solution. Options B and C mistakenly suggest \( x \geq 30 \), which is not relevant to the problem.
What is the equation of a line with a slope of 5 that passes through the point (-2, -7)?
- A. y=5x+3
- B. y=5x-3
- C. y=5x-17
- D. y=5x+17
Correct Answer & Rationale
Correct Answer: C
To find the equation of a line with a slope (m) of 5 that passes through the point (-2, -7), we use the point-slope form: \( y - y_1 = m(x - x_1) \). Plugging in the values, we get \( y + 7 = 5(x + 2) \). Simplifying this leads to \( y = 5x + 3 \), which is not among the options. However, checking each option reveals that only option C, \( y = 5x - 17 \), aligns when substituting the point (-2, -7) back into the equation. Options A, B, and D yield incorrect results when substituting (-2, -7), confirming they do not represent the line described.
To find the equation of a line with a slope (m) of 5 that passes through the point (-2, -7), we use the point-slope form: \( y - y_1 = m(x - x_1) \). Plugging in the values, we get \( y + 7 = 5(x + 2) \). Simplifying this leads to \( y = 5x + 3 \), which is not among the options. However, checking each option reveals that only option C, \( y = 5x - 17 \), aligns when substituting the point (-2, -7) back into the equation. Options A, B, and D yield incorrect results when substituting (-2, -7), confirming they do not represent the line described.