1. Equations of Lines
Lesson 2.2

2. Point Slope Form We seek the equation, given point and slope
(x2, y2) • m
We seek the equation, given point and slope
Recall equation for calculating slope, given two points
Now multiply both sides by (x1 – x2)
Let any point (x,y) on the line be one of the points in the equation

3. Point Slope Form Alternative form Try it out …
For a line through point (6, -2) and slope m = -3/4 determine the equation.
Show both forms
(6, -2) •

4. Slope Intercept Form Recall that we have used y = m * x + b
The b is the y-intercept
Where on the y-axis, the line intersects
m is the slope
Given slope
Observe y-intercept

5. Converting Between Forms
What does it take to convert from point slope form to slope-intercept form?
Multiply through the (x – x1) by m
Simplify the expression
Try it
Note that this also determines the value for the y-intercept, b

6. Two Point Form Given (3, -4) and (-2, 12), determine the equation
Find slope
Use one of the points in the point-slope form

7. Set the style of one of the equations to Thick
Parallel Lines
Given the two equations y = 2x – 5 y = 2x + 7
Graph both equations
How are they the same?
How are they different?
Set the style of one of the equations to Thick

8. Parallel Lines Different: where they cross the y-axis Same: The slope
Note: they are parallel
Parallel lines have the same slope
y=2x+7
y=2x-5
Lines with the same slope are parallel

9. Perpendicular Lines Now consider Graph the lines
How are they different
How are they the same?

10. Perpendicular Lines Same: y-intercept is the same
Different: slope is different
Reset zoom for square
Note lines are perpendicular

11. Perpendicular Lines
Lines with slopes which are negative reciprocals are perpendicular
Perpendicular lines have slopes which are negative reciprocals

12. Horizontal Lines Try graphing y = 3 What is the slope?
How is the line slanted?
Horizontal lines have slope of zero y = 0x + 3

13. Vertical Lines Have the form x = k
What happens when we try to graph such a line on the calculator?
Think about
We say “no slope” or “undefined slope” • k

14. Direct Variation
The variable y is directly proportional to x when: y = k * x
(k is some constant value)
Alternatively
As x gets larger, y must also get larger
keeps the resulting k the same

15. Direct Variation Example:
The harder you hit the baseball
The farther it travels
Distance hit is directly proportional to the force of the hit

16. Direct Variation Suppose the constant of proportionality is 4
Then y = 4 * x
What does the graph of this function look like?
Note:
This is a linear function
The constant of proportionality is the slope
The y-intercept is zero

17. Assignment Lesson 2.2A Page 86 Exercises 1 – 41 odd Lesson 2.2B