Slope of a line joining two points MCQs With Answer

Introduction: Understanding the slope of a line joining two points is essential for B.Pharm students studying coordinate geometry, pharmacy mathematics, and data analysis. The slope (or gradient) quantifies the rate of change between two coordinates and underpins calibration curves, concentration–time plots, and linear approximations in pharmacokinetics. Mastery of slope concepts—calculation using (y2−y1)/(x2−x1), recognizing zero or undefined slopes, and relationships for parallel and perpendicular lines—helps you interpret experimental results and design assays. These targeted MCQs reinforce calculation skills, conceptual understanding, and real-world applications relevant to pharmaceutical studies. Now let’s test your knowledge with 50 MCQs on this topic.

Q1. What is the formula for the slope (m) of a line joining two points (x1, y1) and (x2, y2)?

• m = (x2 − x1)/(y2 − y1)
• m = (y2 − y1)/(x2 − x1)
• m = (x1 + x2)/(y1 + y2)
• m = (y1 − y2)/(x1 + x2)

Correct Answer: m = (y2 − y1)/(x2 − x1)

Q2. What is the slope of the line joining (1, 2) and (3, 6)?

• 1
• 2
• 4
• −2

Correct Answer: 2

Q3. The line joining (2, 5) and (2, 8) has which slope?

• 0
• Undefined (vertical)
• 3/0
• 1

Correct Answer: Undefined (vertical)

Q4. What is the slope of the line joining (0, 0) and (4, 0)?

• Undefined
• 0
• 1
• 4

Correct Answer: 0

Q5. Find the slope of the line joining (−1, 4) and (3, −2).

• −1/2
• −3/2
• 3/2
• 1/2

Correct Answer: −3/2

Q6. The slope and gradient are synonymous in coordinate geometry. Which is correct?

• They are different; slope ≠ gradient
• Slope = gradient
• Gradient is the reciprocal of slope
• Gradient applies only to curves

Correct Answer: Slope = gradient

Q7. If a line has slope 3, what does it indicate about the line’s behavior from left to right?

• The line decreases from left to right
• The line increases from left to right
• The line is horizontal
• The line is vertical

Correct Answer: The line increases from left to right

Q8. What is the slope of a line perpendicular to a line with slope 2?

• 2
• −2
• −1/2
• 1/2

Correct Answer: −1/2

Q9. Two lines are parallel if their slopes are which of the following?

• Negative reciprocals
• Equal
• Both zero
• Opposite signs

Correct Answer: Equal

Q10. For which condition is the slope of the line joining two points equal to zero?

• x1 = x2
• y1 = y2
• x1 + x2 = 0
• y1 − y2 = x1 − x2

Correct Answer: y1 = y2

Q11. What is the slope joining (1, a) and (3, a) (a is constant)?

• a
• 2a
• 0
• Cannot be determined

Correct Answer: 0

Q12. Which equation represents the point–slope form of a line with slope m through (x1, y1)?

• y = mx + c
• y − y1 = m(x − x1)
• x − x1 = m(y − y1)
• mx + y = c

Correct Answer: y − y1 = m(x − x1)

Q13. In pharmaceutical calibration curves (concentration vs. absorbance), the slope represents:

• Baseline noise
• Instrument intercept
• Sensitivity (change in absorbance per concentration unit)
• Total concentration

Correct Answer: Sensitivity (change in absorbance per concentration unit)

Q14. Find the slope between (1/2, 1) and (3/2, 4).

• 1
• 2
• 3
• 4

Correct Answer: 3

Q15. Compute the slope joining (−2, 3) and (4, −9).

• −2
• 2
• −3
• 3

Correct Answer: −2

Q16. For points (t, 2t) and (2t, 5t) where t ≠ 0, the slope is:

• t
• 2
• 3
• 3/t

Correct Answer: 3

Q17. Are the points (0, 0), (1, 2), (2, 4) collinear?

• Yes, because slopes between consecutive points are equal
• No, because y-values are not equal
• Yes, because x-values are equal
• No, because slopes alternate

Correct Answer: Yes, because slopes between consecutive points are equal

Q18. If the slope between two points is undefined, which type of line do they determine?

• Horizontal
• Vertical
• Diagonal with slope 1
• None of the above

Correct Answer: Vertical

Q19. The slope of a line is equal to which trigonometric ratio of the angle θ it makes with the positive x-axis?

• Sine (sin θ)
• Cosine (cos θ)
• Tangent (tan θ)
• Secant (sec θ)

Correct Answer: Tangent (tan θ)

Q20. A line that makes a 45° angle with the x-axis has a slope of:

• 0
• 1
• √2
• −1

Correct Answer: 1

Q21. In coordinate geometry, slope is best interpreted as:

• The y-intercept
• The rise over run (change in y per unit change in x)
• The area under the line
• The product of coordinates

Correct Answer: The rise over run (change in y per unit change in x)

Q22. What is the slope of the line joining (1, 1) and (−1, −1)?

• 0
• −1
• 1
• 2

Correct Answer: 1

Q23. Does swapping the order of two points change the numeric value of the slope?

• Yes, it changes the sign
• No, the slope remains the same
• Yes, it takes the reciprocal
• No, it becomes undefined

Correct Answer: No, the slope remains the same

Q24. The slope of a line perpendicular to y = (3/4)x + 2 is:

• 3/4
• −3/4
• −4/3
• 4/3

Correct Answer: −4/3

Q25. Find the slope joining (0, 5) and (5, 0).

• 1
• −1
• 5
• −5

Correct Answer: −1

Q26. A line has slope 0.5 and passes through (2, 3). What is its y-intercept?

• 1
• 2
• 3
• 4

Correct Answer: 2

Q27. The slope between (x1, y1) and (x2, y2) is negative when:

• (y2 − y1) and (x2 − x1) have the same sign
• (y2 − y1) and (x2 − x1) have opposite signs
• y2 = y1
• x2 = x1

Correct Answer: (y2 − y1) and (x2 − x1) have opposite signs

Q28. Which term correctly describes an infinitely large slope (vertical line)?

• Zero slope
• Undefined slope
• Negative slope
• Reciprocal slope

Correct Answer: Undefined slope

Q29. Slope of the line joining (1, 4) and (4, 1) is:

• 1
• −1
• 3/3
• −3

Correct Answer: −1

Q30. If two lines have slopes m1 = 2 and m2 = 1/2, are they perpendicular?

• Yes, always
• No, because product is 1 not −1
• Yes, because reciprocals indicate perpendicularity
• No, because both are positive

Correct Answer: No, because product is 1 not −1

Q31. A line has x-intercept 3 and y-intercept 6. Its slope is:

• 2
• −2
• −1/2
• 1/2

Correct Answer: −2

Q32. For the linear function f(x) = 2x + 1, the slope of the secant between x = 1 and x = 3 is:

• 1
• 2
• 3
• 4

Correct Answer: 2

Q33. In pharmacokinetics, the slope of a concentration–time plot during a linear elimination phase represents:

• Elimination half-life
• Instantaneous concentration
• Rate of change of concentration with time (elimination rate)
• Bioavailability

Correct Answer: Rate of change of concentration with time (elimination rate)

Q34. Compute the slope joining (1, 1) and (2, 4).

• 1
• 2
• 3
• 4

Correct Answer: 3

Q35. Find the slope between (−1/2, 2) and (3/2, −4).

• −3
• 3
• −6
• −1/3

Correct Answer: −3

Q36. The perpendicular to a vertical line is always:

• Vertical
• Horizontal
• Undefined
• Diagonal with slope 1

Correct Answer: Horizontal

Q37. If a line has slope 0, the line is:

• Vertical
• Horizontal
• Increasing at rate 0
• Undefined

Correct Answer: Horizontal

Q38. For points (k, 2k) and (3k, 5k) with k ≠ 0, the slope equals:

• 3/2
• 2/3
• k
• 5/3

Correct Answer: 3/2

Q39. The slope of the line given by 2x + 3y − 6 = 0 is:

• 2/3
• −2/3
• 3/2
• −3/2

Correct Answer: −2/3

Q40. The average rate of change (slope of a secant) between two concentration points on a curve represents:

• Instantaneous rate at a point
• Average rate over the interval
• Total area under the curve
• Maximum concentration

Correct Answer: Average rate over the interval

Q41. If slope AB = slope BC for three distinct points A, B, C (with distinct x-values), what can be concluded?

• Points A, B, C are collinear
• They form a right triangle
• They lie on a circle
• No conclusion

Correct Answer: Points A, B, C are collinear

Q42. In the line equation y = mx + c, the parameter m denotes:

• The y-intercept
• The slope
• The x-intercept
• The midpoint

Correct Answer: The slope

Q43. Two points with identical x-coordinates always produce which slope?

• Zero
• Undefined
• One
• Negative

Correct Answer: Undefined

Q44. A positive slope indicates:

• The function decreases as x increases
• The function increases as x increases
• A horizontal line
• An undefined behavior

Correct Answer: The function increases as x increases

Q45. What is the slope of the line joining (10, 2) and (5, 7)?

• 1
• −1
• 5
• −5

Correct Answer: −1

Q46. A line has slope −3 and passes through (1, 4). Which is its equation?

• y = −3x + 7
• y = −3x − 7
• y = 3x + 1
• y = −x + 4

Correct Answer: y = −3x + 7

Q47. The slope joining (0, 2) and (2, 6) equals:

• 1
• 2
• 4
• −2

Correct Answer: 2

Q48. A line makes an angle of 135° with the positive x-axis. Its slope is:

• 1
• −1
• √3
• −√3

Correct Answer: −1

Q49. The slope of a line perpendicular to y = −(1/4)x + 1 is:

• −1/4
• 1/4
• 4
• −4

Correct Answer: 4

Q50. Compute the slope joining (3, 7) and (7, −1).

• 2
• −2
• −4
• 4

Correct Answer: −2

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