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# Properties of straight lines

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### Properties of straight lines

1. 1. PROPERTIES OF STRAIGHT LINES <ul><li>Forms of Equation of a Line </li></ul><ul><li>Slope and its Properties </li></ul><ul><li>Intercepts </li></ul>TOPIC 7
2. 2. Definition: Straight Lines - is the line that does not change direction. Slope of a Line - also called as gradient of straight line. It is the measure of the ratio of the vertical change to the horizontal change. x –Intercept - is the point where the graph of the line crosses the x – axis. y –Intercept - is the point where the graph of the line crosses the y – axis.
3. 3. Forms of Equation of a Line FORM NAME EXAMPLE ax + by + c = 0 General form 2x + 4y + 8 = 0 ax + by = c y – y 1 =m(x – x 1 ) y =mx + b Standard form Point-slope form Slope-intercept Intercept form Two point form 2x + 4y = - 8 y - 4 = -½(x-12) y = -½x - 2
4. 4. Lets do these: 1. Tell what form of equation of a straight line Is being given by each equation. 2. 3. 4. 5. 6. 7. 8. 9. 10. General form Standard form Point-slope form Intercept form Slope-intercept Two point form General form Slope-intercept Standard form Point-slope form
5. 5. Gradient (Slope) of a Straight Line Gradient (also called Slope ) of a straight line shows how steep a straight line is. or Symbol used m =
6. 6. Different Types of Gradients ( Slope ) of a Straight Line. 1. A line going up from left to right * rise is positive, and run is positive Slope or Gradient ( m ) is positive rise run
7. 7. 2. A line going down from left to right * Down is negative , and run is positive Slope or Gradient ( m ) is negative down run
8. 8. 3. A line that goes straight across Slope or Gradient ( m ) is zero
9. 9. 4. A line straight up and down Slope or Gradient ( m ) is undefined * Division by zero is not possible.
10. 10. Find the gradient(slope) of the line given by the graph. rise 7 run 4 Gradient = Gradient =
11. 11. m = change in y change in x Gradient = Gradient = Find the gradient(slope) of the line Given by the graph. 4 -2
12. 12. Find the gradient (slope) of these lines: a.
13. 13. Find the gradient (slope) of these lines: b.
14. 14. Find the gradient (slope) of these lines: c.
15. 15. Find the gradient (slope) of these lines: d.
16. 16. Find the gradient(slope) of the line given by points on the graph. ( -1, 8 ) ( 7, -1 ) m -1 - 8 = ( x 1 , y 1 ) ( x 2 , y 2 ) 7 – (-1) - 9 m = 8
17. 17. Use the Slope Formula to find the gradient : a. m =
18. 18. Use the Slope Formula to find the gradient : b. m =
19. 19. Use the Slope Formula to find the gradient : c. m = 6
20. 20. Use the Slope Formula to find the gradient : d. m = -1
21. 21. x – intercept = 0 X - Intercept of a Straight Line The X - intercept of a straight line is simply where the line crosses the x - axis.
22. 22. Identify the x – intercept of these lines: a. x - intercept = none
23. 23. Identify the x – intercept of these lines: b. x - intercept = 0
24. 24. Identify the x – intercept of these lines: c. x - intercept = -5
25. 25. Identify the x – intercept of these lines: d. x - intercept = 5
26. 26. Y - Intercept of a Straight Line The Y intercept of a straight line is simply where the line crosses the Y axis. = 1
27. 27. Identify the Y-intercept of these lines: a. Y- intercept = -2
28. 28. Identify the Y-intercept of these lines: b. y - intercept = 0
29. 29. Identify the Y-intercept of these lines: c. y - intercept = none
30. 30. Identify the Y-intercept of these lines: d. y - intercept = -3