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

2. With a ruler, draw any line
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
- 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

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. 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

12. 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.

13. 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.