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C1: The Equation of a Straight Line

C1: The Equation of a Straight Line. Learning Objective : to be able to find the equation of a straight line and to express it in different forms. Starter:. On axes from -5 to 5, sketch the straight lines: y = 3 x = 2 x = -1 y = x y = x + 2 What is the equation of the x-axis?.

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C1: The Equation of a Straight Line

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  1. C1: The Equation of a Straight Line Learning Objective : to be able to find the equation of a straight line and to express it in different forms

  2. Starter: On axes from -5 to 5, sketch the straight lines: y = 3 x = 2 x = -1 y = x y = x + 2 What is the equation of the x-axis?

  3. The equation of a straight line y m 1 c 0 x The equation of a straight line can be written in several forms. You are probably most familiar with the equation written in the form y = mx + c. The value of m tells us the gradient of the line. The value of c tells us where the line cuts the y-axis. This is called the y-interceptand it has the coordinates (0, c). For example, the line y = 3x + 4 has a gradient of 3 and crosses they-axis at the point (0, 4).

  4. The equation of a straight line One more way to give the equation of a straight line is in the form ax + by + c = 0. This form is often used when the required equation contains fractions. For example, the equation can be rewritten without fractions as 4y – 3x + 2 = 0. It is important to note that any straight line can be written in the form ax + by + c = 0. In particular, equations of the form x = c can be written in the form ax + by + c = 0 but cannot be written in the form y = mx + c.

  5. Example Express the line 3x + 5y – 12 = 0 in the form y = mx + c and hence state the gradient and intercept of the line. 3x + 5y – 12 = 0 5y = -3x + 12 y = -3/5 x + 12/5 Hence, gradient = -3/5 or – 0.6, intercept = 12/5 or 2.4

  6. Task 1 : Work out the gradient and intercept of these lines • y = -2x + 5 • y = 7 – x • y = -2/3 x • 2x – 4y + 5 = 0 • 10x – 5y + 1 = 0 • -x + 2y – 4 = 0 • 7x – 2y + 3 = 0 • 9x + 6y + 2 = 0

  7. Task 2 : Write these lines in the form ax + by + c = 0 • y = 4x + 3 • y = 3x -2 • y = -6x +7 • y = 4/5 x – 6 • y = 7/3 x • y = 2x – 4/7 • y = 2/3 x + 5/6 • y = 3/5 x + ½

  8. Task 3 • A line is parallel to the line y = 5x + 8 and its intercept on the y-axis is (0,3). Write down the equation of the line. • The line y = 6x – 18 meets the x-axis at point P. Work out the co-ordinates of P. • A line is parallel to the the line y = -2/5 x + 1 and its intercept on the y –axis is (0, -4). Work out the equation of the line. Write your answer in the form ax + by + c = 0 where a, b and c are integers.

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