Slope/gradient of a line MCQs With Answer

Slope/gradient of a line MCQs With Answer provides B. Pharm students a clear, practical guide to understanding slopes, gradients, and their applications in pharmaceutical calculations. This Student-friendly post covers slope formula, slope-intercept and standard forms, parallel and perpendicular relationships, and real-world interpretations like concentration–time rates and calibration curves. Designed for pharmacy undergraduates, the questions emphasize calculation, graph interpretation, and applied scenarios relevant to drug kinetics and laboratory data. Each MCQ reinforces core concepts and problem-solving steps to build confidence for exams and lab work. Now let’s test your knowledge with 50 MCQs on this topic.

Q1. What is the slope of the line passing through the points (2, 3) and (5, 11)?

• 8/3
• 3/8
• 2
• -8/3

Correct Answer: 8/3

Q2. What is the gradient (slope) of the line given by y = 4x + 5?

• 5
• 4
• -4
• 1/4

Correct Answer: 4

Q3. For the equation 3x – 2y + 6 = 0, what is the slope?

• -3/2
• 2/3
• 3/2
• -2/3

Correct Answer: 3/2

Q4. What is the slope of a horizontal line y = 7?

• 0
• 7
• Undefined
• -7

Correct Answer: 0

Q5. The line x = -2 has what gradient?

• 0
• Undefined
• -2
• Infinity (represented as 0)

Correct Answer: Undefined

Q6. Find the slope of the line through (-1, 4) and (3, -2).

• -3/2
• 3/2
• -1/2
• 2/3

Correct Answer: -3/2

Q7. Lines parallel to y = -2x + 1 have which slope?

• -1/2
• -2
• 2
• 1/2

Correct Answer: -2

Q8. The slope of a line perpendicular to y = (1/3)x – 4 is:

• -3
• 3
• -1/3
• 1/3

Correct Answer: -3

Q9. What is the slope of the line joining the origin (0,0) and the point (4, 5)?

• 5/4
• 4/5
• 1
• -5/4

Correct Answer: 5/4

Q10. A line has x-intercept 2 and y-intercept 6. What is its slope?

• -3
• 3
• 1/3
• -1/3

Correct Answer: -3

Q11. Convert x + y = 0 to slope-intercept form and identify the slope.

• 0
• 1
• -1
• Undefined

Correct Answer: -1

Q12. What is the equation of a line with slope 2 passing through (1, 3)?

• y = 2x + 1
• y = 2x – 1
• y = x + 2
• y = -2x + 5

Correct Answer: y = 2x + 1

Q13. The slope of the line through (0, -1) and (4, 3) is:

• 1
• -1
• 4
• -4

Correct Answer: 1

Q14. Which statement gives the slope of a line perpendicular to a line with slope m (m ≠ 0)?

• Same as m
• Negative reciprocal, -1/m
• Reciprocal, 1/m
• Opposite, -m

Correct Answer: Negative reciprocal, -1/m

Q15. If a line makes an angle of 45° with the positive x-axis, its slope is approximately:

• 0
• 1
• √3
• 1/√3

Correct Answer: 1

Q16. For 2x + 3y – 12 = 0, the gradient is:

• 2/3
• -3/2
• -2/3
• 3/2

Correct Answer: -2/3

Q17. If two points share the same x-coordinate, the slope between them is:

• Zero
• Undefined
• Equal to y difference
• One

Correct Answer: Undefined

Q18. Slope is best described as which of the following?

• Run divided by rise
• Rise divided by run
• Product of rise and run
• Difference between rise and run

Correct Answer: Rise divided by run

Q19. On a concentration vs time graph, a negative slope indicates:

• Concentration is increasing with time
• Concentration is decreasing with time
• Concentration remains constant
• Measurement error only

Correct Answer: Concentration is decreasing with time

Q20. The slope of the line y = tan(60°) x equals:

• 1
• √3
• 1/√3
• 0.5

Correct Answer: √3

Q21. A calibration curve has equation y = 0.25x + 0.02 (absorbance vs concentration in µg/mL). The slope 0.25 represents:

• Absorbance per µg (sensitivity)
• Concentration per absorbance
• Intercept error
• Time per concentration

Correct Answer: Absorbance per µg (sensitivity)

Q22. If slope = 0 for a drug-release profile segment, this implies:

• Drug concentration is increasing
• Drug concentration remains constant (zero rate)
• Drug concentration is decreasing rapidly
• Instrument malfunction only

Correct Answer: Drug concentration remains constant (zero rate)

Q23. The line passing through (2, -3) and (2, 5) is:

• Horizontal
• Vertical
• Diagonal with slope 1
• Diagonal with slope -1

Correct Answer: Vertical

Q24. If two lines have equal slopes, they are:

• Perpendicular
• Parallel (unless identical)
• Intersecting at right angle
• Coincident only if intercepts differ

Correct Answer: Parallel (unless identical)

Q25. The slope of y = (−5)x is:

• 0
• −5
• 5
• Undefined

Correct Answer: −5

Q26. For points (1.5, 2.0) and (3.0, 5.5), the slope is:

• 2.0
• 3.5
• 1.0
• −1.0

Correct Answer: 2.0

Q27. The slope of the line joining (−2, −4) and (4, 2) equals:

• 1
• −1
• 2/3
• −6

Correct Answer: 1

Q28. A best-fit straight line for concentration vs dilution has slope 0.8. Doubling the concentration will change absorbance by approximately:

• 0.8 units
• 1.6 units
• 0.4 units
• Cannot determine

Correct Answer: 1.6 units

Q29. If a line has equation y = mx and passes through (2, 6), m equals:

• 3
• 6
• 4
• 2

Correct Answer: 3

Q30. The slope of the perpendicular bisector of the segment joining (0, 2) and (4, 2) is:

• 0
• Undefined
• 1/2
• −1/2

Correct Answer: Undefined

Q31. For the standard form 4x − y + 8 = 0, the slope is:

• 4
• −4
• −1/4
• 1/4

Correct Answer: 4

Q32. Which slope corresponds to the steepest line rising to the right?

• 0.5
• 1
• 2
• −3

Correct Answer: 2

Q33. A line through (−1, 0) and (2, 3) has slope:

• 1
• 3/3
• 1/1
• 1

Correct Answer: 1

Q34. If an HPLC calibration line has slope 0.015 AU per µg/mL and intercept 0.002, the concentration for absorbance 0.152 is approximately:

• (0.152 − 0.002)/0.015 ≈ 10 µg/mL
• (0.152 + 0.002)/0.015 ≈ 10.27 µg/mL
• (0.152)/0.015 ≈ 10.13 µg/mL
• Cannot calculate without units

Correct Answer: (0.152 − 0.002)/0.015 ≈ 10 µg/mL

Q35. Which of the following slopes indicates a line falling to the right?

• 0.75
• −0.75
• 1.2
• 0

Correct Answer: −0.75

Q36. The slope of the line given by y = (7/4)x − 2 is:

• 7/4
• 4/7
• −7/4
• −4/7

Correct Answer: 7/4

Q37. Which is true: the slope between points A and B equals the slope between B and C only when:

• Points are collinear
• Points form a triangle
• Segments are perpendicular
• All y-values equal

Correct Answer: Points are collinear

Q38. For a line y = mx + c, increasing m while keeping c constant will:

• Rotate the line steeper about the y-intercept
• Shift the line up
• Shift the line right
• Make the line horizontal

Correct Answer: Rotate the line steeper about the y-intercept

Q39. If two lines have slopes 2 and −1/2 respectively, they are:

• Parallel
• Perpendicular
• Coincident
• Neither parallel nor perpendicular

Correct Answer: Perpendicular

Q40. The slope of a line through (10, 0) and (0, 5) equals:

• −1/2
• 1/2
• −5/10
• 5/10

Correct Answer: −1/2

Q41. For logistic approximations using a linear segment, slope represents:

• Absolute amount only
• Rate of change per unit independent variable
• Intercept error
• Curvature measure

Correct Answer: Rate of change per unit independent variable

Q42. If line L1 has slope 0.6 and L2 is parallel to L1 but passes through (0, 4), what is L2 equation?

• y = 0.6x
• y = 0.6x + 4
• y = 4x + 0.6
• y = −0.6x + 4

Correct Answer: y = 0.6x + 4

Q43. The slope of the line joining (−3, 9) and (3, −9) is:

• −2
• −3
• −9/6
• −3

Correct Answer: −3

Q44. Which slope value corresponds to a line making approximately 63.4° with the x-axis (tan θ ≈ 2)?

• 2
• 0.5
• 63.4
• 1/2

Correct Answer: 2

Q45. For interpolation between (1,2) and (4,8), slope used in linear interpolation is:

• 2
• 6/3
• 2
• Both 2 and 6/3 represent 2

Correct Answer: Both 2 and 6/3 represent 2

Q46. A dissolution test shows concentration rising linearly from 0 to 30 µg/mL in 15 minutes. The slope in µg/mL per minute is:

• 0.5
• 2
• 15
• 0

Correct Answer: 2

Q47. The slope of the line connecting intercepts (a, 0) and (0, b) equals:

• b/a
• −b/a
• a/b
• −a/b

Correct Answer: −b/a

Q48. If a titration pH vs volume curve segment is approximated by y = −0.8x + 7, what does slope −0.8 represent?

• pH increase per mL added
• pH decrease per mL added
• Absolute pH only
• Equivalence point volume

Correct Answer: pH decrease per mL added

Q49. Two points are (0.25, 1.75) and (1.25, 3.25). The slope is:

• 1.5
• 1.25
• 1.0
• 2.0

Correct Answer: 1.5

Q50. A line has slope m and passes through (x0, y0). The point-slope form is:

• y = mx + b
• y − y0 = m(x − x0)
• x − x0 = m(y − y0)
• y = m(x0) + y0

Correct Answer: y − y0 = m(x − x0)

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