10.7.1a Slope Intercept Form

Last chapter, we saw that you can graph a line provided that you know the starting point (a coordinate) and the slope (which allows you to find other coordinates).  If the starting point is the y-intercept of the line, then there is specific format called the slope intercept form:

y = mx + b

Resources:

• 10.7.1a: Notes. Slope Intercept Form Part I
• Graphing Equations App
• Desmos online graphing tool

Homework:

• p349 #1, 2, 4, 6, 8, 11, 14, 17

Things you should know after today:

• the relationship between the equation of a line and each of the coordinates on the line
• how to determine the slope and y-intercept from an equation in slope intercept form
• write an equation in slope intercept form a graph or if you are given the slope and the y-intercept

10.7.1b Slope Intercept Form

If a line is not in slope intercept form, it is possible to graph it by isolating your y variable.

Resources

• Notes

Assignment

• P349 #3, 5, 7, 9. 10. 12, 13, *16 *20, *21

After today's lesson, you should be able to:

• convert an equation that is not in slope intercept form into slope intercept form by isolading algebraically for y.
• understand the relationship between the equation of a line and each of the coordinates that is on the line.

10.7.2 General Form

Slope intercept form is best when you know the y-intercept and the slope of a line, but there are many times, especially when talking about real life situations, that we don't know what the slope or the y-intercept are.

Suppose you have 2 jobs that each pays different hourly wages.  Job X pays $10 per hour, and job Y pays $12 per hour.  How many hours do you need to work at each job to earn $2000?  While the relationship would represent a straight line, it may not be easy to determine the slope and y-intercept immediately.

Today we will learn about the general form: 

Ax + By + C = 0

We will also learn about the 2 special cases:

• horizontal line
• vertical line

Resources

• Notes

Assignment

• P365 #1, 2-3 (ace), 4-5, #6ace, #7, 10-14, 18, 19, *15, *16, 

After today, you should be able to:

• change an equation in slope-intercept form into general form
• use the general form to find the x and y intercepts
• draw the graph of a line if you are given general form
• draw graphs of special cases (vertical and horizontal lines)

Attachments:

File	Description	File size
10.7.2.notes.general.form.pdf		3959 kB

10.7.3 Slope Point Form

If you have a graph and want to find the equation for the line, sometimes the y-intercept is not an integer and it is hard to find the equation.  Similarly, you can't really find the equation in general form if you only have the graph.

The slope-point form of the equation of a line is the most useful as it only requires the slope and ANY coordinate on the line.

y-y₁ = m(x-x₁)

Furthermore, it is easy to convert slope point form into both y-intercept and general forms.

Resources

• Notes
• Review of the 3 forms for the equation of a line

Assignment

• P377 #1-3(ac) #4, #5-6(ac) #7, 8, 10, 11,    #13, 15, 16, 17, 22,  *19, 20

After today's lesson, you should be able to:

• convert between all 3 forms for the equation of a line (slope-intercept, general and slope-point)
• Graph a line given the equation in slope-point form
• Write the equation of a line in slope-point form if you are given:
  • two coordinates
  • a coordinate and a slope

Attachments:

File	Description	File size
10.7.3.notes.2011.pdf		712 kB
10.7.5.review.key.pdf		1288 kB

10.7.4 Parallel and Perpendicular Lines

Resources

• Notes

Assignment

• p377 #1-3(ac) #4, #5-6(ac) #7, 8, 10, 11, #13, 15, 16, 17, 22, *19, 20;

After today you should be able to:

• explain how the slopes of parallel lines are related
• explain how the slopes of perpendcular lines are related
• find the equation of a parallel line given an initial line and a point
• find the equation of a perpendicular line given an initial line and a point

Attachments:

File	Description	File size
10.7.4.notes.parallel.pdf		700 kB

10.7.5 Review

Assignment

• P396    #1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13-17

Attachments:

File	Description	File size
10.7.5.review.key.pdf		1288 kB