An introduction to slope. In Unit 5 we are introduced to the concept of slope and linear equations. We began with the topic of linear equations and graphs. Remember that the word linear mean "line" and that all linear equations, when graphed form a straight line.
Here are my notes on linear equations and graphs--------->
We first had to find an equation from a table. Remember that we actually did this when we found the nth term in Unit 1. We just didn't call it an equation then.
Here is a great worksheet that explores the difference between a function and a relation.
In the next section 5-4 we begin to look at forms of linear equations. You will learn 3:
1. Slope-intercept form 2. Standard form 3. Point-slope form
All 3 of these forms have their own unique characteristics that make them worthy of learning. The first of the three is the Slope-intercept form. This form is perhaps the most widely used and recognized in Algebra because it offers the most useful information, i.e. the slope and y-intercept.
You MUST be able to graph a line with an equation in slope-intercept form. This is a skill that will follow you throughout every math you take.
The second form of a linear equation that you must know is Standard form. Ax+By=C. This form is useful for showing where the x and y intercepts are. Just plug in 0 for x to find the y-intercept and 0 for y to find the x-intercept. Standard form is probably the most underrated form of a linear equation. You begin to appreciate it more the more you use it. Here are the notes for that section.
The last form of a linear equation that you must know is Point-slope form. Like slope-intercept form, this form has two parts: the slope and a point. That's all you need to write this equation- no intercept needed! Like all forms of linear equations, you should be able to graph them no matter what form. You should also be comfortable changing from one form to another in order to identify certain parts of the line. For example. Make sure you can go from point-slope form to slope-intercept form to identify the y-intercept.
The last two things that you need to know in Unit 5 are that: 1. Parallel lines have the same slope. 2. Perpendicular lines have opposite and reciprocal slopes.
What does that mean? Well, take a look at my notes to find out.
Unit 5
An introduction to slope.
In Unit 5 we are introduced to the concept of slope and linear equations. We began with the topic of linear equations and graphs. Remember that the word linear mean "line" and that all linear equations, when graphed form a straight line.
Here are my notes on linear equations and graphs--------->
We first had to find an equation from a table. Remember that we actually did this when we found the nth term in Unit 1. We just didn't call it an equation then.
Here is a great worksheet that explores the difference between a function and a relation.
In the second section we learned how to quickly find the slope between two points using the very very important slope formula.
Here are the notes for Section 5-2
Here are the notes and practice sheet for finding the direct and inverse variation. You should complete this worksheet for homework.
5.3 Rate of Change and Direct Variation.pdf
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Inverse Practice.pdf
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In the next section 5-4 we begin to look at forms of linear equations. You will learn 3:
1. Slope-intercept form2. Standard form
3. Point-slope form
All 3 of these forms have their own unique characteristics that make them worthy of learning. The first of the three is the Slope-intercept form. This form is perhaps the most widely used and recognized in Algebra because it offers the most useful information, i.e. the slope and y-intercept.
Here are the notes for that section.
You MUST be able to graph a line with an equation in slope-intercept form. This is a skill that will follow you throughout every math you take.
The second form of a linear equation that you must know is Standard form. Ax+By=C. This form is useful for showing where the x and y intercepts are. Just plug in 0 for x to find the y-intercept and 0 for y to find the x-intercept. Standard form is probably the most underrated form of a linear equation. You begin to appreciate it more the more you use it.
Here are the notes for that section.
The last form of a linear equation that you must know is Point-slope form. Like slope-intercept form, this form has two parts: the slope and a point. That's all you need to write this equation- no intercept needed! Like all forms of linear equations, you should be able to graph them no matter what form. You should also be comfortable changing from one form to another in order to identify certain parts of the line. For example. Make sure you can go from point-slope form to slope-intercept form to identify the y-intercept.
Here are the notes for point-slope form.
The last two things that you need to know in Unit 5 are that:
1. Parallel lines have the same slope.
2. Perpendicular lines have opposite and reciprocal slopes.
What does that mean? Well, take a look at my notes to find out.
Here is a practice worksheet involving parallel and perpendicular lines and their slopes.
Here are a bunch of practice worksheets if you would like some more help in this Unit.
That finishes Unit 5.