3.6 Notes – Lines in the Coordinate Plane (Pg 166)
Lesson Objectives:
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By Postulate 1-1 (in chapter 1) you need _________________________ to determine a line.
Graphing Lines in Slope-Intercept Form
A. What does ‘m’ represent in the equation y = mx +b?
B. What does ‘slope’ mean when you’re talking about a line?
C. What does the ‘b’ represent in the equation y = mx + b?
D. What is an ‘intercept’ on a graph?
E. Use this equation for questions 1-3: y 
3
x2.
4
1. What is the slope of this line? Explain what that means.
2. What is the y-intercept of this line? Explain what that means.
3. Graph the line:
 Label your x- and y-axis
 Draw a point at the y-intercept of the line.
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From that point, use your slope to find the next point (remember: slope =

Use a straightedge to connect the two points! That is your line!
rise
).
run
1
F. Use the following equation to answer questions 4 and 5: y   x  2
2
4. What is different about the slope of this line? What is that going to do to the graph of your line?
5. Graph the line.
Graphing Lines in Standard Form (Using Intercepts)
A. How many points do you need to graph a line? _______
B. Name 5 ordered pairs – (x, y) – that lie on the x-axis. What pattern do you notice?
C. Name 5 ordered pairs – (x, y) – that lie on the y-axis. What pattern do you notice?
D. Use the following equation to answer questions 1-4: 6 x  3 y  12
1. What form is the equation in (slope-intercept, standard, point-slope)?
2. If you wanted to find the x-intercept (where the line crosses the x-axis), what would your y-value
have to be?
3. If you wanted to find the y-intercept (where the line crosses the y-axis), what would your x-value
have to be?
4. Find the x- and y-intercepts of the equation. Use those to graph the line (Look at Page 167
Example 2 in your book to do this problem!):
E. Graph the following equation using the intercepts:  2 x  4 y  8
Graphing Lines in Standard Form (Transforming to Slope-Intercept)
F. Use the following equation to answer questions 1-3: 4 x  2 y  9
1. What is slope-intercept form?
2. Transform the given equation into slope-intercept form (hint: what variable do you have to solve
for?)
3. Now that the equation is in slope intercept form, graph it:
G. Graph the following equation by transforming it into slope-intercept form:  5 x  y  3