Slope–intercept form of a line MCQs With Answer

The slope–intercept form of a line (y = mx + b) is a fundamental algebraic tool B.Pharm students use to analyze linear relationships in pharmacy — from calibration curves and dissolution rates to concentration–time approximations and dose–response windows. Understanding slope (m) and intercept (b) helps interpret rate of change, initial values, and graph behavior in experimental data and quality control. These MCQs emphasize practical applications, stepwise conversions between forms, graph reading, and problem-solving relevant to pharmacokinetics and analytical assays. Clear comprehension of this form streamlines data analysis and supports accurate reporting in labs and research. Now let’s test your knowledge with 50 MCQs on this topic.

Q1. What is the slope–intercept form of a straight line?

• y = mx + b
• ax^2 + bx + c = 0
• x = my + b
• y – y1 = m(x – x1)

Correct Answer: y = mx + b

Q2. In the equation y = 3x + 5, what is the slope?

• 5
• 3
• -3
• 0

Correct Answer: 3

Q3. In y = -2x + 7, what is the y-intercept?

• -2
• 7
• 0
• -7

Correct Answer: 7

Q4. Convert the standard form 2x – y = 4 to slope–intercept form.

• y = -2x + 4
• y = 2x – 4
• y = 4x – 2
• y = -4x + 2

Correct Answer: y = 2x – 4

Q5. What is the slope of the line through points (1, 2) and (3, 6)?

• 1
• 2
• 4
• -2

Correct Answer: 2

Q6. Which slope gives a line parallel to y = 4x + 1?

• -4
• 1/4
• 4
• 0

Correct Answer: 4

Q7. What is the slope of a line perpendicular to y = (1/2)x – 3?

• 2
• -2
• 1/2
• -1/2

Correct Answer: -2

Q8. Find the x-intercept of y = 3x – 9.

• 0
• 3
• -3
• 9

Correct Answer: 3

Q9. A line with slope 0 represents which of the following?

• Vertical line
• Diagonal line rising left to right
• Horizontal line
• Perpendicular line

Correct Answer: Horizontal line

Q10. If a line passes through (0, -5), what is its y-intercept?

• -5
• 0
• 5
• Cannot be determined

Correct Answer: -5

Q11. Write the equation of a line with slope -3 and y-intercept 4.

• y = -3x + 4
• y = 3x – 4
• y = -4x + 3
• y = 4x – 3

Correct Answer: y = -3x + 4

Q12. For the pharmacokinetic approximation y = -0.2t + 10, what does the slope represent?

• Initial concentration
• Rate of concentration decrease per unit time
• Time to reach zero concentration
• Half-life directly

Correct Answer: Rate of concentration decrease per unit time

Q13. In dose–response linear regions, the slope typically indicates which property?

• Baseline response
• Change in response per unit dose (sensitivity)
• Maximum possible response
• Time delay to response

Correct Answer: Change in response per unit dose (sensitivity)

Q14. Convert y + 2 = 5(x – 1) to slope–intercept form.

• y = 5x + 7
• y = 5x – 7
• y = 5x – 3
• y = -5x + 3

Correct Answer: y = 5x – 7

Q15. For y = (2/3)x + 9, what is y when x = 3?

• 11
• 9
• 3
• 15

Correct Answer: 11

Q16. For y = -4x + 12, find x when y = 0.

• 3
• -3
• 12
• 0

Correct Answer: 3

Q17. Which equation is NOT a slope–intercept form?

• y = 2x + 1
• y = ax^2 + b
• y = -x + 3
• y = 0.5x – 4

Correct Answer: y = ax^2 + b

Q18. If the slope of a line is positive, the line:

• Decreases left to right
• Is horizontal
• Increases left to right
• Is vertical

Correct Answer: Increases left to right

Q19. A line with y-intercept 0 does which of the following?

• Passes through origin
• Has slope 0
• Is vertical
• Has no x-intercept

Correct Answer: Passes through origin

Q20. The slope of a vertical line is:

• 0
• Undefined
• 1
• -1

Correct Answer: Undefined

Q21. How does absolute slope magnitude relate to graph steepness?

• Smaller magnitude means steeper
• Larger magnitude means steeper
• Magnitude has no effect
• Only sign affects steepness

Correct Answer: Larger magnitude means steeper

Q22. Given concentration-time points (0, 50) and (5, 40), what is the slope (units per hour)?

• -2
• 2
• -10
• 10

Correct Answer: -2

Q23. Evaluate y for x = 4 in y = 0.5x + 2.

• 4
• 6
• 2
• 0

Correct Answer: 4

Q24. Convert x + 3y = 6 to slope–intercept form; what is the slope?

• 3
• -3
• -1/3
• 1/3

Correct Answer: -1/3

Q25. In y = -0.01x + 1 describing fraction remaining, the intercept 1 most likely means:

• Steep decline rate
• Initial fraction at time zero
• Half-life in hours
• Zero concentration

Correct Answer: Initial fraction at time zero

Q26. Are the lines y = 2x + 3 and y = 2x – 4 parallel?

• No, different slopes
• Yes, same slope different intercepts
• They are perpendicular
• They are identical

Correct Answer: Yes, same slope different intercepts

Q27. Are the lines y = (1/2)x + 5 and y = -2x + 5 perpendicular?

• Yes
• No, slopes are equal
• No, both positive slopes
• They are parallel

Correct Answer: Yes

Q28. A line with slope 1 typically makes which angle with the positive x-axis (in ideal square graph units)?

• 0 degrees
• 45 degrees
• 90 degrees
• 30 degrees

Correct Answer: 45 degrees

Q29. Find equation of line with slope 4 passing through (2, 3).

• y = 4x – 5
• y = 3x + 2
• y = 4x + 11
• y = x + 1

Correct Answer: y = 4x – 5

Q30. Solve y = mx + b for x.

• x = my + b
• x = (y – b)/m
• x = (b – y)/m
• x = y + b

Correct Answer: x = (y – b)/m

Q31. Which form is quickest to read y-intercept from?

• Point-slope form
• Slope–intercept form
• Standard form with no rearrangement
• Quadratic form

Correct Answer: Slope–intercept form

Q32. For standard form Ax + By = C, what is the slope in terms of A and B?

• A/B
• -A/B
• B/A
• -B/A

Correct Answer: -A/B

Q33. What is the slope of the line through points (1,1) and (1,4)?

• 0
• Undefined (vertical)
• 3
• -3

Correct Answer: Undefined (vertical)

Q34. A slope magnitude close to zero indicates the line is:

• Very steep
• Nearly horizontal
• Vertical
• Perpendicular to x-axis

Correct Answer: Nearly horizontal

Q35. If slopes of two lines multiply to -1, the lines are:

• Parallel
• Perpendicular
• Coincident
• Orthogonal only if intercepts match

Correct Answer: Perpendicular

Q36. In zero-order drug elimination approximated as linear decline, the slope m corresponds to:

• The elimination rate constant in first-order kinetics
• The constant rate of loss (k0) with negative sign
• The half-life directly
• Logarithmic slope

Correct Answer: The constant rate of loss (k0) with negative sign

Q37. On a semilog concentration vs time plot, a straight line indicates:

• Zero-order kinetics
• First-order kinetics and slope related to -k/2.303
• No kinetic information
• Nonlinear elimination

Correct Answer: First-order kinetics and slope related to -k/2.303

Q38. Which statement about y = -5x + 0 is true?

• y-intercept is -5
• Line passes through origin
• Slope is 0
• Line is vertical

Correct Answer: Line passes through origin

Q39. Rewrite y = 7 – 2x in slope–intercept standard order and identify the slope.

• y = -2x + 7; slope -2
• y = 2x + 7; slope 2
• y = -7 + 2x; slope 2
• y = 7 + 2x; slope 2

Correct Answer: y = -2x + 7; slope -2

Q40. Interpolate y at x = 2.5 between points (2, 5) and (3, 3) using slope–intercept logic.

• 5.5
• 4
• 3.5
• 2

Correct Answer: 4

Q41. In an analytical calibration graph, what does a steeper slope indicate?

• Lower sensitivity to concentration changes
• Higher sensitivity to concentration changes
• Higher intercept value only
• No relation to sensitivity

Correct Answer: Higher sensitivity to concentration changes

Q42. Given point (x, y) = (4, 10) and slope m = 2, how do you compute b?

• b = x – my
• b = y – mx
• b = y + mx
• b = mx – y

Correct Answer: b = y – mx

Q43. If you multiply both m and b by constant k ≠ 1, what happens to the line?

• Line remains identical
• Line shifts and slope changes; not the same line
• Only intercept changes
• Only slope changes but intercept same

Correct Answer: Line shifts and slope changes; not the same line

Q44. If rise = 4 and run = 2, what is the slope?

• 2
• 0.5
• -2
• 8

Correct Answer: 2

Q45. How can slope–intercept form help estimate initial concentration from linear experimental data?

• Intercept b gives the estimated initial concentration at time zero
• Slope gives the initial concentration directly
• Product of m and b is initial concentration
• Only standard form can be used

Correct Answer: Intercept b gives the estimated initial concentration at time zero

Q46. Convert 6x – 2y = 8 into slope–intercept form; what is the y-intercept?

• -4
• 4
• 3
• -3

Correct Answer: -4

Q47. What is the slope of the line through (0, 0) and (4, 2)?

• 0.5
• 2
• 4
• 8

Correct Answer: 0.5

Q48. For y = -1/4 x + 5, evaluate y at x = 8.

• 3
• 7
• 4
• -3

Correct Answer: 3

Q49. A negative slope indicates the function:

• Increases left to right
• Decreases left to right
• Is constant
• Is undefined

Correct Answer: Decreases left to right

Q50. Identify slope and intercept for y = (3/4)x – 1.

• Slope 3/4; intercept -1
• Slope -1; intercept 3/4
• Slope 4/3; intercept -1
• Slope 3/4; intercept 1

Correct Answer: Slope 3/4; intercept -1

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