Linear Graphs y = mx + c (Edexcel IGCSE Maths A)

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  • What does the constant m represent in the equation of a straight line y equals m x plus c?

    In the equation of a straight line y equals m x plus c, the constant m represents the gradient of the line.

  • True or False?

    In the equation of a line y equals m x plus c, the constant c tells you where the line crosses the x-axis.

    False.

    In the equation of a line y equals m x plus c, the constant c tells you where the line crosses the y-axis.

  • What two bits of information do you need to find the equation of a straight line?

    To find the equation of a straight line you need:

    • the gradient of the line

    • a point on the line (it could be the y-intercept)

  • Define the term y-intercept.

    The y-intercept is where a graph crosses the y-axis.

  • True or False?

    The constant c in the equation of a line a x plus b y plus c equals 0 refers to the y-intercept.

    False.

    The constant c in the equation of a line a x plus b y plus c equals 0 does not refer to the y-intercept.

    You need to rearrange it to make y the subject.

  • How do you find the equation of a line if you know the gradient and a point on the line?

    If you know the gradient of a line and a point on the line, then to find the equation:

    • write y equals m x plus c where m is the gradient

    • Substitute the coordinates of the point into the equation for x and y

    • Solve the equation to find c

  • How can you find the equation of a straight line if you have the coordinates of two points on the line?

    If you have the coordinates of two points on a straight line then you can find the equation of the line y equals m x plus c.

    1. Find the gradient, m, using the coordinates (e.g. form a right-angled triangle)

    2. Substitute one pair of coordinates into y equals m x plus c to find c

  • True or False?

    The gradient of the line with the equation 2 x plus y plus 5 equals 0 is 2.

    False.

    The gradient of the line with the equation 2 x plus y plus 5 equals 0 is not 2. You need to write it in the form y equals m x plus c first, giving y equals negative 2 x minus 5. Therefore the gradient is -2.

  • How do you sketch the line a x plus b y equals c?

    To sketch the line a x plus b y equals c:

    • Substitute x equals 0 to find where it crosses the y-axis

    • Substitute y equals 0 to find where it crosses the x-axis

    • Draw a line going through the two intercepts

    You could also find any other two points on the line and use those.

  • How do you sketch the line y equals m x plus c?

    To sketch the line y equals m x plus c:

    • plot the point open parentheses 0 comma space c close parentheses

    • find another point by substituting in another value for x

    • plot that point and draw a straight line going through both points

    You can also use the gradient; for every one unit to the right, go up/down by m.

  • What does a line with a negative gradient look like?

    A line with a negative gradient will start at the top left and go down to the bottom right.

  • If two lines are parallel then what is the relationship between the gradients of the lines?

    If two lines are parallel then their gradients are equal.

  • True or False?

    The lines y equals 4 x plus 5 and y equals 3 x plus 5 are parallel.

    False.

    The lines y equals 4 x plus 5 and y equals 3 x plus 5 are not parallel because the gradients are different. They both have the same y-intercept.

  • How do you find the equation of a line if you know a point on the line and you know the equation of a line it is parallel to?

    If you know a point on a line and you know the equation of a line it is parallel to then you can find the equation of the line:

    • m is equal to the gradient of the parallel line

    • substitute the coordinates of the point into y equals m x plus c and solve to find c

  • What is the gradient of a line that is parallel to the line y equals 3 x minus 2?

    The gradient of a line that is parallel to the line y equals 3 x minus 2 is 3.

  • Define perpendicular lines.

    Two perpendicular lines intersect at right angles (90°).

  • The lines y equals m x plus c and y equals M x plus C are perpendicular. State the relationship between m and M.

    If the lines y equals m x plus c and y equals M x plus C are perpendicular, then m cross times M equals negative 1.

    This can be written as m equals negative 1 over M or M equals negative 1 over m.

    The gradients are negative reciprocals of one another.

  • True or False?

    The lines y equals 2 x plus 3 and y equals 1 half x plus 1 are perpendicular.

    False.

    The lines y equals 2 x plus 3 and y equals 1 half x plus 1 are not perpendicular.

    This is because 2 cross times 1 half equals 1 not negative 1.

    y equals 2 x plus 3 and y equals negative 1 half x plus 1 would be perpendicular.

  • What is the gradient of a line that is perpendicular to the line y equals 3 x minus 2?

    The gradient of a line that is perpendicular to the line y equals 3 x minus 2 is negative 1 third.

  • True or False?

    The line y equals 5 is perpendicular to the line x equals 4.

    True.

    The line y equals 5 is perpendicular to the line x equals 4. The first line is horizontal and the second is vertical.