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Equation of a Straight Line

Equation of a Straight Line. Given an equation of the form y = mx + c. Find the value of x , when y = 0. Step 1:. Equation of a Straight Line. Example:. Solution:. Draw the graph of y = x + 2. y. When y = 0,. 2. 0 = x + 2 x = – 2. 1. x. O. – 2. – 1. 1.

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Equation of a Straight Line

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  1. Equation of a Straight Line

  2. Given an equation of the form y = mx + c Find the value of x, when y = 0. Step 1: Equation of a Straight Line Example: Solution: Draw the graph of y = x + 2. y When y = 0, 2 0 = x + 2 x = – 2 1 x O – 2 – 1 1

  3. Given an equation of the form y = mx + c Find the value of y, when x = 0. Step 2: Equation of a Straight Line Example: Solution: Draw the graph of y = x + 2. y y 2 When x = 0, 1 y = 0 + 2 = 2 x O – 2 – 1 1

  4. Equation of a Straight Line Given an equation of the form y = mx + c Example: Solution: Step 3: Draw the graph of y = x + 2. y Draw a straight line which passes through the two points. 2 1 x Remarks: You can choose any other two suitable points. O – 2 – 1 1

  5. Determining whether a given point lies on a straight line the coordinates of the point satisfy the equation of the straight line. Equation of a Straight Line If a point lies on a straight line,

  6. Example The same Equation of a Straight Line Determine whether the point (2, 9) lies on the straight line 2y = 5x + 8. Solution: 2y = 5x + 8 Substitute y = 9 Substitute x = 2 2(9) = 18 5(2) + 8 = 18

  7. Example Equation of a Straight Line Determine whether the point (2, 9) lies on the straight line 2y = 5x + 8. Conclusion: Left hand side = Right hand side x = 2 and y = 9 satisfy the equation 2y = 5x + 8.  The point (2, 9) lies on the straight line 2y = 5x + 8.

  8. Given the gradient and y-intercept Gradient y-intercept Equation of a Straight Line y = mx + c

  9. Example I: Gradient y-intercept m = 3 c = – 2 Equation of a Straight Line Write the equation of the straight line given: Gradient = 3, y-intercept = –2 y = x 3 – 2

  10. Example II: 1 y-intercept Gradient 4 (0, c) = (0, 7) m = c = 7 Equation of a Straight Line Write the equation of the straight line given: Gradient = and passes through the point (0, 7) y = x+ 7 + 7

  11. Given the equation in the form y = mx + c y-intercept Gradient m = –2 c =constant term = 5 Equation of a Straight Line Determine the gradient and the y-intercept of the straight line: y = –2x+ 5

  12. Given the equation of the form ax + by = c Make y as the subject Write in the form: y = mx + c Equation of a Straight Line Determine the gradient and the y-intercept of the straight line: 3x + 5y = 15 – 3x + 15 3 5y = –3x + 15 5 5 y = y =–x + 3

  13. Gradient y-intercept c = 3 m = – Equation of a Straight Line Given the equation of the form ax + by = c Determine the gradient and the y-intercept of the straight line: 3 3 5 5 y =–x + 3

  14. Straight line that is parallel to the x-axis y 4 A B y-intercept = 3 2 – 4 – 2 2 x Equation of a Straight Line State the equation of the straight line AB. y = 3 Answer: O If the y-intercept of a straight line which is parallel to the x-axis is k, then the equation of the straight line is y = k.

  15. Straight line that is parallel to the y-axis y 4 A x-intercept = –5 2 – 4 – 2 2 x B Equation of a Straight Line State the equation of the straight line AB. x = –5 Answer: O If the x-intercept of a straight line which is parallel to the y-axis is h, then the equation of the straight line is x = h.

  16. A straight line that passes through a given point and has a specific gradient Step 1: Substitute the value of m. Equation of a Straight Line Find the equation of the straight line which passes through the point (– 1, 2) and has a gradient of 2. Solution: y = 2x + c

  17. A straight line that passes through a given point and has a specific gradient Step 2: Substitute the x-coordinate and the y-coordinate into the equation to find c. Equation of a Straight Line Find the equation of the straight line which passes through the point (– 1, 2) and has a gradient of 2. Solution: 2 = 2(–1)+ c c = 4

  18. A straight line that passes through a given point and has a specific gradient Step 3: Write the equation with the values of m and c. Equation of a Straight Line Find the equation of the straight line which passes through the point (– 1, 2) and has a gradient of 2. Solution: y = 2x + 4

  19. A straight line that passes through two given points Step 1: Find the gradient, m, from the formula: Equation of a Straight Line Find the equation of the straight line which passes through point (1, 2) and point (3, 8). Solution: m = 3

  20. A straight line that passes through two given points Step 2: Substitute the value of m. Equation of a Straight Line Find the equation of the straight line which passes through point (1, 2) and point (3, 8). Solution: y = 3x + c

  21. A straight line that passes through two given points Step 3: Substitute the x-coordinate and the y-coordinate from either point into the equation to find c. Equation of a Straight Line Find the equation of the straight line which passes through point (1, 2) and point (3, 8). Solution: 2 = 3(1)+ c c = –1

  22. A straight line that passes through two given points Step 4: Write the equation with the values of m and c. Equation of a Straight Line Find the equation of the straight line which passes through point (1, 2) and point (3, 8). Solution: y = 3x– 1

  23. The point of intersection of two straight lines y From the graph, the point of intersection is (–1, –2). 4 2 x – 4 – 2 2 Equation of a Straight Line Find the point of intersection of two straight lines y = 3x + 1 and x + y = –3. Graphical Method y = 3x + 1 O x + y = –3

  24. The point of intersection of two straight lines Equation of a Straight Line Find the point of intersection of two straight lines y = 3x + 1 and x + y = –3. Solving simultaneous equation Step 1: y = 3x + 1 … … x + y = –3 … … Substitute y = 3x + 1 into equation x + 3x + 1 = –3 4x = –4 x = –1

  25. The point of intersection of two straight lines Equation of a Straight Line Find the point of intersection of two straight lines y = 3x + 1 and x + y = –3: Solving simultaneous equation Step 2: Substitute x = –1 into equation  y = 3(–1) + 1 = –2

  26. The point of intersection of two straight lines Equation of a Straight Line Find the point of intersection of two straight lines y = 3x + 1 and x + y = –3: Solving simultaneous equation Answer The point of intersection of the two straight lines is (–1, –2).

  27. The End

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