Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Slope-Intercept Form A.CED.2

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Essential Questions: How do I write the equation of a line in slope- intercept form? How do I graph a line of an equation in the slope-intercept form?

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms slope-intercept form : y = mx + b x-intercept: where the line crosses the x-axis y-intercept: where the line crosses the y-axis

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. What is an intercept? Y intercept Y= -4 (0, -4) X intercept X = 4 (4,0)

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Slope-Intercept Form y = mx + b “M” is slope and “b” is y-intercept

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Y = mx + b M is the slope B is the y-intercept Leave x and y, simply x and y. You must have an “x” and “y” !!

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Use the slope intercept form to construct a graph of y=2x - 8 What is the slope and y-intercept? Slope is 2, and y intercept is (0,-8) Graph the y intercept and then use the slope of 2 (convert into 2/1) and rise 2 and run 1 to get your second point. Connect the two points and add arrows!

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Write an equation in slope-intercept form for a line. A line contains the points (–1, 3) and (2, –3). Find m. Substitute for x, y, and m in the equation y = mx + b. 3 = –2(–1) + b m = –3 – 3 2 – (–1) –6 3 = –2= b = 1 y = –2x + 1 y = mx + b

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Write an equation in slope intercept form ( y = mx + b) Use the points (3,3) and (5,7) First find the slope using the formula. The slope is 2. Now, choose a point so that you can substitute for x, y, AND m to be able to find b. 3 = 2 ( 3) + b solve for b. B is –3 So the equation is y = 2x - 3

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Summarizer and Review! Graph an equation in slope-intercept form. y = –2x + 1 m = –2; b = 1 Graph the y-intercept (0, 1). Move 1 unit right and 2 units down to locate (1, –1). Draw the line through (0, 1) and (1, –1). TOC

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Intercepts When finding the x-intercept, y=0 When finding the y-intercept, x=0 Example y= 4x – 5 Find the x and y intercepts:

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Finding the x-intercept Remember the x-intercept is where the line crosses the x-axis What can you tell me about ANY x intercept? What is the x-intercept of this line?

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Do this: Y= -3x + 12 Find the x and y intercepts. ( y is easy!) Y intercept is 12 (0, 12) To find the x intercept, substitute 0 for y. So the x intercept is 4 (4, 0) Note: y intercepts always have a 0 for x Note: x intercepts always have a 0 for y

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Try Another! Y = 2x – 18 Find the x and y intercepts Y = -18 The ordered pair is (0,-18) Find the x intercept (sub. 0 in for y) 0 = 2x – 18 X =9 The ordered pair is (9,0)

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Try these Find the intercepts for Y = -4x + 8 The intercepts are (0,8) and (2,0) Y= 3x – 15 The intercepts are (0,-15) and (5,0)

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Writing equations for Horizontal Lines Consider the slope intercept form of a line Y = mx +b What is the slope (m) of a horizontal line? 0 So we know m is going to be zero. Y = 0(x) + b Y = b (use this for any horizontal line!)

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Lets try! What is b (the y-intercept of this line)? B is 4. Y=4 is your equation.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Same idea applies for vertical lines What is the x-intercept of this line? 3! X=3 is the equation! Remember, the slope of a vertical line is undefined!

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Write the equations for these lines. Y=-3X = -2

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Summarizer How can you determine the equation of a line if all you see is the graph? Find the y-intercept and let be “b”. Calculate rise/run to determine the slope “m” Write in the from Y=mx + b

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Homework Work book pg , #’s 1-33 all

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. HW Answers: 1.5; 5 2.2; ; ; ; ; /

Copyright © by Holt, Rinehart and Winston. All Rights Reserved Graphs 28. c 29. B 30. A Graphs