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.. 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 Slope = Slope =
Homework Plot the points and draw a line through the given points. Find the slope of the line.. A(-,2) and B(-,-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,) and B( 2,2) 6. A(-3,5) and B(,) What type of slope do the following lines have? 7. 8. 9.
Aim: How do we write an equation of a line? Warm Up:.Simplify: 3x(2x+8) 2. Simplify: (4x 3 )(8x -2 ) 3. Estimate 20% of $22.56 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.. 2. 3. 4. 5. 6. 7. 8.
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:. Slope = 4 2. Slope = 3. Slope = /3 4. Slope = -3 y-inter = -3 y inter = 8 y inter = -2 y inter = 5 2 5. Slope = -7 6. Slope = ½ 7. Slope = 8. Slope = 3 5 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.. y = 3x + 2 2. y = -5x + 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.. 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 = Equation Equation Equation
0. Given y = -3x + 5, what is the slope of the line?. Given y = -4x -7, what is the y -intercept of the line? 2. Given y = x 4, what is the slope? 3. If the slope of a line is ½ and the y-intercepts is 3, what is the equation of the line? 4. What is the slope of a line whose equation is y = ½x - 2? 5. What is the slope and y-intercept of a line whose equation is y = x + 4? 3 Draw the line through the given points and find the slope. 6. A(,2) and B(,-4) 7. A(3,4) and B(-3,-5) 8. A(5,-4) and B(-5,4) Write the equation of the line given: 9. 20. m = -6 and b = 2 2. m = 5 3 and b = 4 22. m = 3 and b = -4 23. m = 2 and b = 0 24. The slope is and the y-intercept is -. 4 Homework p. 647 #-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.. 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. 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. 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 #0-22 even
Aim: How do we write a linear equation in standard form? Warm Up:. 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.. 3x + y = 8 2. x + y = 2 3. 4x 2y = 8 4. 2x y = 8 5. 4x = y + 8 6. y 3x = 0 7. 3x + 3y = 5 8. 3y 2x = 27 9. 5x + y = 6 0. 4x + y = -2. x + y = 6 2. -2x + y = 5 Write in standard form and Graph using slope/y-intercept. 3. y 2x = -5 4. 2x + y = 4 5. -2x + 4y = -6
Standard Form Homework Write in Standard Form.. 2x + y = 5 2. x + 2y = 2 3. 3x 4y = 8 4. x y = 7 5. 3x = y + 6. y 4x = 4 7. 5x + 5y = 5 8. 9y 2x = 2 Write in standard form and Graph 9. 3x + 2y = 6 0. 4x + 3y = -2. x + 2y = 6
Aim: How do we graph a linear equation using a table? Warm Up: Quiz A. Steps for Graphing a linear equations using a table:. 2. 3. 4.. y = 2x - 5 2. y = 3 x + 2 x y (x,y) x y (x,y) 3. 2x + y = 4. 4y + 2x = 6 x y (x,y) x y (x,y)
Graph each line using a table of values. Table Method Homework. y = 3x - 6 2. y = 2 x + x y (x,y) x y (x,y) 3. -3x + y = -4 4. 3y + 6x = 9 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 ) x y -2 7-6 0 5 2 2) x y -2-7 - -4 0-2 3) x y -2 - - 0 0 2
4) x y -2 8-6 0 4 2 5) x y -2-4 - -2 0 0 2 6) x y -2-6 - -5 0-4 2 Homework Function Rule Ditto
Graphing Review. 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: 2 3. y = x 4 4. y + 7 = -3x 5. y 2x = 8 6. y + 5 = x 3 7. x + y = 6 Given the slope and y-intercept, write the equation of each line. 8. Slope = -4 9. Slope = 0. Slope = 8. Slope = ½ y-inter = 2 y inter = 0 y inter = -3 y inter = 5 Find the slope of each line. 2. 3. 4. Graph each line. 5. y = 3x - 5 6. y = ½x 3 7. y = -x + 4 8. 2x + y = 5
9. Given the equation: y = -3x + 5 complete the table and graph the equation. x Y=-3x + 5 y (x,y) Write a function rule for each: 20. x y 5 35 7 39 9 43 2 47 23 5 2. x 3 4 5 6 7 y 7 23 29 35 4 22. Solve: 3(x + 3) 2x = 3x 4 23. Solve: 9x + 6 = 7x 24. A $48 shirt is on sale for 30% off. Find the sale price. 25. Simplify: (3x -5 )(7x 8 ) 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 30 x 60 x