Complete the following problems in your lecture notebook, QUIETLY.1) Find the slope of the line given (2, 3) and (-3, -2).
2) Write the equation y – 5 = 6(x – 8) in slope-intercept form.
3) Write the equation y + 7 = -8(x + 5) in slope-intercept form.
Announcements:•Unit 1 Retake is tomorrow after school.•Unit 1 Test Corrections are due 9/19/12.
Do Now
Students will be able to demonstrate their understanding of graphing linear
equations by correctly graphing at least 3 of the 4 linear equations on their exit slip.
Objective
Ex. x – y = 6 y = x – 6
• Step 1: Plot your y-intercept on your graph.
• Step 2: Rewrite your slope as a fraction.
• Step 3: The numerator is the vertical change (RISE) & the denominator is the horizontal change (RUN).
• Step 4: Graph at least 2 points and connect the dots.
Rules for Graphing in Slope-intercept formy = mx + b
• Step 1: Rewrite your equation in slope-intercept form.
• Follow the steps for Graphing in slope-intercept form.
Rules for Graphing in Standard form.Ax + By = C
Example 1: Graph y = ½x – 7.
Step 1 The y-intercept is –7. So graph (0, –7).
From (0, –7), move up 1 unit and right 2 units. Draw a dot.
Step 3 Draw a line through the points.
Step 2 The slope is 1/2 .
Example 2: Graph 5x + 4y = 8.
Step 2 The y-intercept is 2, so graph (0, 2).
From (0, 2), move down 5 units and right 4 units. Draw a dot. Draw a line connecting the points.
Step 3 The slope is
Step 1 Write the equation in slope-intercept form
Example 3: Graph the line given the slope & y-intercept.
y intercept = 4
Step 1 The y-intercept is 4, so the line contains (0, 4). Plot (0, 4).
Step 3 Draw the line through the two points.
•
••
•
Run = 5
Rise = –2
Step 2 Slope = Count
2 units down and 5 units right
from (0, 4) and plot another point.
y
slope = 4; y-intercept =
Step 1 The y-intercept is , so the
line contains (0, ). Plot (0, ).
Step 3 Draw the line through the two points.
•
•Rise = 4
Run = 1
Example 4: Graph the line given the slope and y-intercept.
Step 2 Slope = Count
4 units up and 1 unit right from
(0, ) and plot another point.
Example 5: Graph y = 3x – 1 slope: m = 3 =
y-intercept: b = –1
Step 1 Plot (0, –1).
Step 2 Count 3 units up and 1 unit right and plot another point.
Step 3 Draw the line connecting the two points.
•
•
Example 6: Graph 2y + 3x = 6
Step 1 Write the equation in slope-intercept form.
Step 2 Graph the line.
slope: m =
y-intercept: b = 3
Plot (0, 3). •
•
Step 3 Count 3 units down and 2 units right and plot another point. Draw the line connecting the two points.
YOU TRY! #1
Graph the line given the slope and y-intercept.
slope = 2, y-intercept = –3
Step 1 The y-intercept is –3, so the line contains (0, –3). Plot (0, –3).
•
•
Step 3 Draw the line through the two points.
Rise = 2
Run = 1Step 2 Slope =
Count 2 units up and 1 unit right
from (0, –3) and plot another
point.
Graph each line given the slope and y-intercept.
slope = , y-intercept = 1
YOU TRY! #2
Step 1 The y-intercept is 1, so the line contains (0, 1). Plot (0, 1).
•
Step 3 Draw the line through the two points.
•
Rise = –2
Run = 3
Step 2 Slope = Count 2 units down and 3 units right from (0, 1) and plot another point.
YOU TRY! #3Graph the line described by the equation.
Step 1 Plot (0, 0).
Step 2 Count 2 units up and 3 units right and plot another point.
Step 3 Draw the line connecting the two points.
y = x + 0 is in slope-intercept form slope: m = 2/3 &
y-intercept: b = 0
•
•
YOU TRY! #4
6x + 2y = 10
Step 1 Write the equation in slope intercept form.
Write the equation in slope-intercept form. Then graph the line described by the equation.
Step 2 Graph the line.
y-intercept: b = 0
• Plot (0, 5).
slope: m =
• Count 3 units down and 1 unit right and plot another point.
• Draw the line connecting the two points.
•
•
y = –3x + 5
YOU TRY! #5
y = –4
Step 1 Plot (0, –4).
y = –4 is in the form y = mx + b.
y-intercept: b = –4
slope: m = 0 = = 0
Since the slope is 0, the line will be a horizontal at y = –4. •
Graph the line described by the equation.
Graph y = 2x – 4YOU TRY! #6
Graph 3x + 2y = 6.YOU TRY! #7
Write the equation in slope-intercept form and then graph the line. 6x + 2y = 10
y = –3x + 5
Reminder by the end of this lesson you will be expected to do this.
