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Linear Functions & Graphs (DP IB Analysis & Approaches (AA))

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  • FrontEquations of a Straight Line

    What is the formula for calculating the gradient of a straight line?

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  • What is the formula for calculating the gradient of a straight line?

    The formula for calculating the gradient of a straight line is m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction

    Where:

    • m is the gradient of the line

    • open parentheses x subscript 1 comma space y subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 close parentheses are two different points on the line

    This is given in your exam formula booklet.

  • What does 'c' represent in the gradient-intercept form of the equation of a straight line?

    The 'c' in the gradient-intercept form of the equation of a straight line represents the y-coordinate of the point at which the line intersects the y-axis (y-intercept).

  • State the point-gradient form of a straight line equation.

    The point-gradient form of a straight line equation is open parentheses y minus y subscript 1 close parentheses equals m open parentheses x minus x subscript 1 close parentheses

    Where:

    • m is the gradient of the line

    • open parentheses x comma space y close parentheses are the coordinates of any point on the line

    • open parentheses x subscript 1 comma space y subscript 1 close parentheses are the coordinates of a specific point on the line

    This is given in your exam formula booklet.

  • How can you find the x-intercept from the general form of a linear equation, a x plus b y plus d equals 0?

    The x-intercept from the general form of a linear equation, a x plus b y plus d equals 0is open parentheses negative d over a comma space 0 close parentheses.

    This comes from substituting in y equals 0 and then solving for x to get x equals negative d over a.

  • Define parallel lines.

    Parallel lines are lines that are always equidistant and never intersect.

  • What is the relationship between the gradients of parallel lines?

    Parallel lines have the same gradient.

  • True or False?

    If two lines are parallel, their y-intercepts must be the same.

    False.

    Parallel lines have the same gradient but can have different y-intercepts.

  • How can you determine if two lines are parallel using their equations?

    Rearrange into y equals m x plus c form and compare the coefficients of x.

    If they are equal, the lines are parallel.

  • What is the gradient of a horizontal line?

    The gradient of a horizontal line is 0.

  • What is the equation of a vertical line?

    The equation of a vertical line is x equals k, where k is a constant.

    E.g. x equals negative 4 is a vertical line that crosses the x-axis at -4.

  • Define perpendicular lines.

    Perpendicular lines are lines that intersect at right angles (90 degrees).

  • What is the relationship between the gradients of perpendicular lines?

    The gradients of perpendicular lines are negative reciprocals of each other.

    E.g. if a line, l subscript 1, has a gradient of -3, then a line, l subscript 2, that is perpendicular to l subscript 1 will have a gradient of 1 third.

Previous:Binomial TheoremNext:Quadratic Functions & Graphs

    1. Topic 1

      Number & Algebra Toolkit

    2. Topic 2

      Exponentials & Logs

    3. Topic 3

      Sequences & Series

    4. Topic 4

      Simple Proof & Reasoning

    5. Topic 5

      Proof by Induction & Contradiction

    6. Topic 6

      Binomial Theorem

    7. Topic 7

      Permutations & Combinations

    8. Topic 8

      Complex Numbers

    9. Topic 9

      Further Complex Numbers

    10. Topic 10

      Systems of Linear Equations

    1. Topic 1

      Linear Functions & Graphs

    2. Topic 2

      Quadratic Functions & Graphs

    3. Topic 3

      Functions Toolkit

    4. Topic 4

      Other Functions & Graphs

    5. Topic 5

      Reciprocal & Rational Functions

    6. Topic 6

      Transformations of Graphs

    7. Topic 7

      Polynomial Functions

    8. Topic 8

      Inequalities

    9. Topic 9

      Modulus Functions & Further Transformations

    1. Topic 1

      Geometry Toolkit

    2. Topic 2

      Geometry of 3D Shapes

    3. Topic 3

      Trigonometry

    4. Topic 4

      The Unit Circle & Exact Values

    5. Topic 5

      Trigonometric Functions & Graphs

    6. Topic 6

      Trigonometric Equations & Identities

    7. Topic 7

      Inverse & Reciprocal Trigonometric Functions

    8. Topic 8

      Trigonometric Proof & Equation Strategies

    9. Topic 9

      Vector Properties

    10. Topic 10

      Vector Equations of Lines

    11. Topic 11

      Vector Planes

    1. Topic 1

      Statistics Toolkit

    2. Topic 2

      Correlation & Regression

    3. Topic 3

      Probability

    4. Topic 4

      Discrete Random Variables

    5. Topic 5

      Binomial Distribution

    6. Topic 6

      Normal Distribution

    7. Topic 7

      Continuous Random Variables

    1. Topic 1

      Differentiation

    2. Topic 2

      Techniques & Applications of Differentiation

    3. Topic 3

      Integration

    4. Topic 4

      Techniques & Applications of Integration

    5. Topic 5

      Optimisation

    6. Topic 6

      Kinematics

    7. Topic 7

      Basic Limits & Continuity

    8. Topic 8

      Further Differentiation

    9. Topic 9

      Further Integration

    10. Topic 10

      Differential Equations

    11. Topic 11

      Maclaurin Series

    12. Topic 12

      Limits using l'Hôpital's Rule & Maclaurin Series