Aim: How do we find the slope of a line?
Warm Up: Go over test
A. Slope - ________________________________________________________
_____________________________________________________________________________Plot the points and draw a line through the given points. Find the slope of the line. 1. A(-5,4) and B(4,-3) 2. A(4,3) and B(4,-6) 3. A(-3,-2) and B(4,4)
For questions 4-8 answer the following questions:
A. What type of slope is represents by the given line? B. Find the slope of each line.
4. 5. 6.
Type ____________ Type _____________ Type ____________
Slope = Slope = Slope =
7. 8.
Type ____________ Type _____________
Homework
Plot the points and draw a line through the given points. Find the slope of the line.
1. A(-1,2) and B(-1,-5) 2. A(4,3) and B(-4,-3) 3. A(5,-2) and B(0,4)
4. A(2,2) and B(4,5) 5. A(-5,1) and B( 2,2) 6. A(-3,5) and B(1,1)
What type of slope do the following lines have?
Aim: How do we write an equation of a line? Warm Up:
1.Simplify: 3x(2x+8) 2. Simplify: (4x3)(8x-2) 3. Estimate 20% of $122.56
A. Writing an Equation from a Graph
To write the equation of a line we need 2 pieces of information: ________________ & _________________
The _____________________ is the point where the line crosses the ________________ The standard equation of a line is _______________________
The m represents the ___________________ The b represents the ____________________
Find the slope, y-intercept, and write the equation for each line.
1. 2. 3.
4. 5. 6.
B. Writing an Equation Given the Slope and y-intercept
What is the standard equation of a line? ______________________
The m represents the _______________ and the b represents the _____________
Write the equation of each line given:
1. Slope = 4 2. Slope = 1 3. Slope = 1/3 4. Slope = -3 y-inter = -3 y –inter = 8 y –inter = -2 y –inter = 5 ______________ __________________ ________________ ______________
5. Slope = -7 6. Slope = ½ 7. Slope = 3 2 8. Slope = 5 1 − y-inter = 0 y –inter = -3 y –inter = -6 y –inter = 6 ______________ __________________ ________________ ______________
C. Find the Slope and y-intercept from an Equation
Find the slope or y-intercept of each line.
1. y = 3x + 2 2. y = -5x + 1 3. y = x – 7 4. y = 2x – 8 Slope = ________ Slope = _______ y –inter = ______ y-inter = _____
5. y = ½ x 6. y = -x + 6 7. y = 2x 8. y = 2x + 4 Slope = ________ Slope = _______ y –inter = ______ y-inter = _____
Equation of a Line – Day 2 Find the slope and y-inercept. Write the equation of each line.
1. 2. 3.
Slope = ______ Slope = ______ Slope = ______
y-inter =_______ y-inter =_______ y-inter =_______
Equation ____________ Equation _____________ Equation _____________
4. 5. 6.
Slope = ______ y-inter =_______ Equation ____________ Equation _____________ Equation __________
7. 8. 9.
Slope = ______ Slope = ______
y-inter =_______ y-inter =_______
10. Given y = -3x + 5, what is the slope of the line? ____________ 11. Given y = -4x -7, what is the y -intercept of the line? ____________ 12. Given y = x – 4, what is the slope? ____________
13. If the slope of a line is ½ and the y-intercepts is 3, what is the equation of the line? _________________
14. What is the slope of a line whose equation is y = ½x - 2? _______________
15. What is the slope and y-intercept of a line whose equation is y = 4? 3 1
+
x _________
Draw the line through the given points and find the slope.
16. A(1,2) and B(1,-4) 17. A(3,4) and B(-3,-5) 18. A(5,-4) and B(-5,4)
Write the equation of the line given:
19. 20. m = -6 and b = 2 21. m = 5 3 and b = 4 22. m = 3 and b = -4 23. m = 2 and b = 0 24. The slope is 4 1
− and the y-intercept is -1.
Homework p. 647 #1-9
Aim: How do we graph a linear equation using the slope and y-intercept? Warm Up: Find the slope and y-intercept of each.
1. y = 3x - 4 2. y = 2x +5 3. y = -4x + 6 4. y = ½x 5. y = x + 4
A. Steps for Graphing using slope/y-intercept 1. Write in slope intercept form y = mx + b 2. Find the slope and y-intercept
3. Plot the y-intercept
4. Use the slope to get additional points (at least 3) 5. Connect and extend
6. Label
1. y =-4x -5 2. y = 3x + 5 3. y= -3x +4 4. y = 2/3 x – 6
5. x = 4 6. y = 3 Give additional examples
Homework (Graph Paper) p.647 #10-22 even
Aim: How do we write a linear equation in standard form?
Warm Up: 1. Given y = 4x – 5, what is the slope of the line? ___________________ 2. If the slope of a line is -2 and the y-intercept is 3, what is the equation of the line? ________________
3. Sketch the graph of a line whose slope is zero. A. Writing Equations in Standard Form (Function Form/ Slope/y-intercept Form)
What is the standard equation of a line? What do the m and b represent?
Write in Standard Form.
1. 3x + y = 8 2. –x + y = 12 3. 4x – 2y = 8 4. 2x – y = 8
5. 4x = y + 8 6. y – 3x = 0 7. 3x + 3y = 15 8. 3y – 2x = 27
9. 5x + y = 16 10. 4x + y = -12 11. –x + y = 6 12. -2x + y = 15
Write in standard form and Graph using slope/y-intercept.
Standard Form Homework Write in Standard Form.
1. 2x + y = 5 2. –x + 2y = 12 3. 3x – 4y = 8 4. x – y = 7
5. 3x = y + 1 6. y – 4x = 4 7. 5x + 5y = 15 8. 9y – 2x = 21
Write in standard form and Graph
Aim: How do we graph a linear equation using a table? Warm Up: Quiz
A. Steps for Graphing a linear equations using a table:
1. _____________________________________________________________________ 2. _____________________________________________________________________ 3. ______________________________________________________________________ 4. ______________________________________________________________________ 1. y = 2x - 5 2. y = 3 1 x + 2 3. 2x + y = 1 4. 4y + 2x = 6 x y (x,y) x y (x,y) x y (x,y) x y (x,y)
Table Method Homework Graph each line using a table of values.
1. y = 3x - 6 2. y = 2 1 x +1 3. -3x + y = -4 4. 3y + 6x = 9 x y (x,y) x y (x,y) x y (x,y) x y (x,y)
Name________________________________________ Function Rule Write the function Rule for each table, find the missing values and graph the line
1) x y -2 7 -1 6 0 5 1 2 ____________________________ 2) x y -2 -7 -1 -4 0 -1 1 2 ____________________________ 3) x y -2 -1 -1 0 0 1 1 2 ____________________________
Homework
Function Rule Ditto
4) x y -2 8 -1 6 0 4 1 2 ____________________________ 5) x y -2 -4 -1 -2 0 0 1 2 ____________________________ 6) x y -2 -6 -1 -5 0 -4 1 2 ____________________________
Graphing Review
1. What is the standard equation of a line? ______________________________ 2. What do the m and b represent in a linear equation? ________________________ Find the slope and y-intercept of each:
3. y = x – 4 4. y + 7 = -3x 5. y – 2x = 8 6. y + 5 = x 3 2
7. –x + y = 6
Given the slope and y-intercept, write the equation of each line.
8. Slope = -4 9. Slope = 1 10. Slope = 8 11. Slope = ½ y-inter = 2 y –inter = 0 y –inter = -3 y –inter = 5 ______________ __________________ ________________ ______________
Find the slope of each line.
12. 13. 14.
Graph each line.
19. Given the equation: y = -3x + 5 complete the table and graph the equation.
Write a function rule for each: 20.
21.
22. Solve: 3(x + 3) – 2x = 3x – 14 23. Solve: 9x + 6 = 7x
24. A $48 shirt is on sale for 30% off. Find the sale price.
25. Simplify: (3x-5)(7x8) 26. What is the complement of 70?
27. What is the measure of ∠x? 28. What is the measure of ∠x? What is the measure of ∠y?
y 130 x 60 x x Y=-3x + 5 y (x,y) x y 15 35 17 39 19 43 21 47 23 51 x 3 4 5 6 7 y 17 23 29 35 41