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Straight Lines Introductory activity

Learn about different types of lines in geometry, calculate slopes, and understand properties of linear functions on a Cartesian Plane. Practice drawing and identifying parallel, perpendicular, and intersecting lines.

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Straight Lines Introductory activity

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  1. Straight LinesIntroductory activity Tools required: • graph paper • ruler Step 1: Draw a Cartesian Plane

  2. Step 2: With a ruler, draw any line

  3. Step 3: Find someone who drew a similar line.

  4. Step 4: • Answer the following questions: • Did you draw an oblique line, or a straight line? • How would you calculate the slope of your line?

  5. Step 5: • On the same Cartesian Plane, draw another line. • What type of lines do you now have? • Parallel lines • Perpendicular lines • Intersecting lines

  6. Vocabulary↔ • Abscissa • Ordinate • Collinear • Direct variation • Partial variation • x-coordinate • y-coordinate • Points are collinear if they are on the same line. All segments of a line have the same slope. • Passes through the origin y = mx • Does not pass through the origin y = mx + b

  7. Definitions • x-intercept: the point at which the line crosses the x-axis. • y-intercept: the point at which the line crosses the y-axis. • Parallel lines: 2 lines that never cross. • Perpendicular lines: 2 lines that cross and make a 90 degree angle.

  8. Slope formula • Standard form: y = mx + b • (x, y): coordinates on the Cartesian Plane • m: slope • b: y-intercept • General form: Ax + By + C = 0 • m: -A /B • b: -C/B

  9. Properties of linear functions Constant function Linear function Oblique line Rule f(x) = mx+b Slope (m) and y-intercept (b) Domain: All real numbers Range: All real numbers • - Horizontal line • Rule f(x) = b • Slope m = 0 • Domain:  (all real numbers) • Range: value of ‘b’

  10. Vertical lines • Not a function as it fails the vertical line test. • Rule x = a • Domain: ‘a’ • Range: All real numbers • X-intercept or zero: ‘a’

  11. y y y y x x x x The slope of a horizontal line is zero and the slope of a vertical line is undefined. Vertical line m = Ø Horizontal line m = 0 Oblique lines have slopes that are in between these – both positive and negative. The graph to the left has a line whose slope is 1. Notice that it makes an angle of 45 with the x-axis. The same can be said for the graph of the line on the right whose slope is -1. m = 1 m = -1

  12. y y y x x x Whenever the incline of the line approaches that of a horizontal line, the slope approaches 0. m = 0 m = 1 m = ¼ Notice that the green line is flatter than the blue line. This means the slope is closer to that of a horizontal line. That is why its slope is ¼, because it is closer to zero.

  13. y y y x x x Whenever the incline of the line approaches that of a vertical line, the slope gets further from 0. m = Ø m = 1 m = 4 Notice that the red line is steeper than the blue line. This means the slope is closer to that of a vertical line. That is why its slope is 4, because it is further from zero.

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