Straight Lines II Introductory activity Tools required: graph paper ruler Step 1: Draw a Cartesian Plane

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

Step 3: Find someone who drew a similar line.

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?

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

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

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.

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

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

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’

The slope of a horizontal line is zero and the slope of a vertical line is undefined. x y x y 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. x y x y m = 1 m = -1

Whenever the incline of the line approaches that of a horizontal line, the slope approaches 0. x y x y x y 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.

Whenever the incline of the line approaches that of a vertical line, the slope gets further from 0. x y x y x y 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.