Question 1
The line through (a, 3) and (5, a) is parallel to the line y = 2x + 1. What is the value of a?
Hard - Quiz 2
Test your mastery with SAT-level problems that layer multiple linear equation concepts into each question, demanding precise reasoning under pressure.
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Answer question 1 to unlock
The line ax - 4y = 12 is perpendicular to the line passing through (1, 6) and (3, 2). What is the value of a?
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Answer question 2 to unlock
A freelance photographer charges a flat booking fee plus an hourly rate. A 2-hour shoot costs $340, and a 5-hour shoot costs $625. How much would a 7-hour shoot cost?
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Answer question 3 to unlock
The line y = kx - 5 and the line 3x + 2y = 14 intersect at a point where y = 1. What is the value of k?
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The line 2x - by = 10 has a y-intercept of (0, -2). What is the value of b, and what is the x-intercept of the line?
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Answer question 5 to unlock
A line passes through the origin and the point (6, k), forming a triangle with the x-axis and the vertical line x = 6. If the area of this triangle is 21 square units and k is positive, what is the equation of the line?
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Answer question 6 to unlock
A line is perpendicular to 5x + 2y = 8 and passes through the point (3, -1). What is the value of x when y = 3 on this line?
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Answer question 7 to unlock
The line y = mx + 4 passes through the intersection of the lines y = 3x - 2 and y = -x + 10. What is the value of m?
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Answer question 8 to unlock
Town A has a population modeled by y = -250x + 10,000 and Town B by y = 500x + 2,500, where x is years since 2015. In what year will the populations be equal, and what will that population be?
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Answer question 9 to unlock
The line through (p, 2p) and (p + 4, 5p - 6) has a slope of 3/2. What is the value of p?
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Answer question 10 to unlock
Line L has the equation y = (3/5)x + b and passes through the midpoint of the segment connecting (2, 8) and (10, 4). What is the x-intercept of line L?
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