4.9 notes alg1.notebook notes alg1.notebook december 04, 2012 4.9 slopes of parallel and...
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4.9 Notes Alg1.notebook December 04, 2012
Skills we've learned
Skills we need
The table shows time spent on homework and number of incorrect quiz answers for several students.
1. Find an equation for a line of best fit. 2. Interpret the meaning of the slope and yintercept. 3. Use your equation to predict the number of incorrect answers for 5 hours of study.4. How well does the line of best fit represent the data? Explain.
49 Slopes of Parallel and Perpendicular Lines
Given two points: (3, 5) and (2, 7), find the equation of a line in1. pointslope2. slopeintercept3. standard form
Warmup AnswersThe table shows time spent on homework and number of incorrect quiz answers for several students.
1. Find an equation for a line of best fit.
2. Interpret the meaning of the slope and yintercept.
3. Use your equation to predict the number of incorrect answers for 5 hours of study.
4. How well does the line of best fit represent the data? Explain.
y ≈ 0.8x + 10.3
slope: for every hour of study, the number of incorrect answers decreases by 0.8; yint.: a student who studies for 0 h will get 10.3 incorrect answers
6.3
Given two points: (3, 5) and (2, 7), find the equation of a line in1. pointslope2. slopeintercept3. standard form
4.9 Notes Alg1.notebook December 04, 2012
4.9 Notes Alg1.notebook December 04, 2012
49 Slopes of Parallel and Perpendicular Lines
2. Write equations to describe lines parallel or perpendicular to a given line.
1. Identify and graph parallel and perpendicular lines.
Geometry!!!
4.9 Notes Alg1.notebook December 04, 2012
4.9 Slopes of Parallel and Perpendicular LinesTo sell at a particular farmers’ market for a year, there is a $100 membership fee. Then you pay $3 for each hour that you sell at the market. However, if you were a member the previous year, the membership fee is reduced to $50.
The red line shows the total cost if you are a new member.
The blue line shows the total cost if you are a returning member.
These two lines are parallel. Parallel lines are lines in the same plane that have no points in common. In other words, they do not intersect.
4.9 Slopes of Parallel and Perpendicular Lines
4.9 Notes Alg1.notebook December 04, 2012
I. Identifying Parallel Lines
1. Identify which lines are parallel.
Write all equations in slopeintercept form to determine the slope.
I. Identifying Parallel Lines
2. Identify which lines are parallel.
Write all equations in slopeintercept form to determine the slope.
Which ones have parallel slopes?
4.9 Notes Alg1.notebook December 04, 2012
I. Identifying Parallel Lines
3. Identify which lines are parallel.
Which ones have parallel slopes?
Your turn...
Write all equations in slopeintercept form to determine the slope.
II. Geometry Application4. Show that JKLM is a parallelogram. Use the ordered pairs and the slope formula to find the slopes of MJ and KL.
MJ is parallel to KL because they have the same slope.
JK is parallel to ML because they are both horizontal.JK is parallel to ML because they are both horizontal.
MJ is parallel to KL because they have the same slope.
Since opposite sides are parallel, JKLM is a parallelogram.
Use the ordered pairs and the slope formula to find the slopes of MJ and KL.
4.9 Notes Alg1.notebook December 04, 2012
II. Geometry Application5. Show that the points A(0, 2), B(4, 2), C(1, –3), D(–3, –3) are the vertices of a parallelogram. Use the ordered pairs and the slope formula to find the slopes of MJ and KL.
Your turn...
Use the ordered pairs and the slope formula to find the slopes of MJ and KL.
III. Identifying Perpendicular Lines
Perpendicular lines are lines that intersect to form right angles (90o).
4.9 Notes Alg1.notebook December 04, 2012
III. Identifying Perpendicular Lines
6. Identify which lines are perpendicular:
The graph described by y = 3 is a horizontal line, and the graph described by x = –2 is a vertical line. These lines are perpendicular.
These lines are perpendicular because the product of their slopes is –1.
III. Identifying Perpendicular Lines
7. Identify which lines are perpendicular:
start here,describe these lines
Your turn...
4.9 Notes Alg1.notebook December 04, 2012
IV. Geometry Application of Perpendicular Lines
8. Show that ABC is a right triangle.If ABC is a right triangle, AB will be perpendicular to AC.
AB is perpendicular to AC because
Therefore, ABC is a right triangle because it contains a right angle.
If ABC is a right triangle, AB will be perpendicular to AC.
V. Equation of Parallel & Perpendicular Lines
10. Write an equation in slopeintercept form for the line that passes through (4, 10) and is parallel to the line described by y = 3x + 8.
Step 1 Find the slope of the line.
Step 2 Write the equation in pointslope form.
Step 3 Write the equation in slopeintercept form.
The parallel line also has a slope of ___
4.9 Notes Alg1.notebook December 04, 2012
11. Write an equation in slopeintercept form for the line that passes through (2, –1) and is perpendicular to the line described by y = 2x – 5.
Step 1 Find the slope of the line.
Step 2 Write the equation in pointslope form.
Step 3 Write the equation in slopeintercept form.
The perpendicular line has a slope of ___
V. Equation of Parallel & Perpendicular Lines
11. Write an equation in slopeintercept form for the line that passes through (–5, 3) and is perpendicular to the line described by y = 5x.
Your turn...
12. Write an equation in slopeintercept form for the line that passes through (5, 7) and is parallel to the line described by y = x – 6.
4.9 Notes Alg1.notebook December 04, 2012
49 p.297 #3 9, 12, 16, 18, 23, 25, 26, 34, 41, 46 48
*18 problems