1 / 31

Warm up 8/24

Warm up 8/24. Solve each equation for y . 1. 7 x + 2 y = 6 2. 3. If 3 x = 4 y + 12, find y when x = 0. 4. If a line passes through (–5, 0) and (0, 2), then it passes through all but which quadrant. y = –2 x – 8. y = –3. IV. Be seated before the bell rings. DESK.

tso
Download Presentation

Warm up 8/24

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Warm up 8/24 Solve each equation for y. 1. 7x + 2y = 6 2. 3. If 3x = 4y + 12, find y when x = 0. 4. If a line passes through (–5, 0) and (0, 2), then it passes through all but which quadrant. y = –2x – 8 y = –3 IV

  2. Be seated before the bell rings DESK Warm-up (in your notes) Agenda: Warmup Go over hw p. 94 & 100 Note 2.3 & 2.4 notes homework • Quiz – Tuesday 8/12 • Tomorrow

  3. Don’t forget test retakes

  4. Notebook 1 Table of content 2.3 Graph linear function/ 2.4 Writing linear functions Page 1) 1-1 Sets of Numbers /1.2 Properties of Numbers 1 2) 1-3 Square Roots 3) 1-4 Simplify Algebra Expression 4) 1.6 Relations/1.7 functions 5) 1.9 Parent Functions 6) 2.1 Linear Equations/ 2.2 Proportions 7) 2.3 & 2.4

  5. 2.3 Graph & (2.4) write linear functions Learning targets • 2.3: I can graph linear equations using slope and a point • 2.3: I can graph linear equations using intercepts • 2.3: I can graph linear equations in slope-intercept form • 2.4: I can write the equation of a line in slope intercept form • 2.4: I can write the equation of parallel and perpendicular lines in slope-intercept form

  6. 2.3 Graph & (2.4) write linear functions How much do you know Write down as many word as you can about linear functions. ______________ ______________ ______________ ______________ ______________ ______________

  7. 2.3 Graph & (2.4) write linear functions Functions 𝟏, 𝟐, and 𝟑 have the tables shown below. Examine each of them, make a conjecture about which will be linear, and justify your claim.

  8. +2 +2 +2 2.3 Graph & (2.4) write linear functions –1 –1 –1 A linear function has a constant rate of change constant rate of change = Slope (m)

  9. Graphing Linear Functions 3 ways to graph: • With y-intercept and slope • With a point and a slope • With x and y-intercepts

  10. Slope-Intercept Form: y=mx+b 1st way Example: y=-3/4x+3

  11. Point & Slope: has a slope m and passes through the point (x,y) 2nd Way Example: slope of 3/2 and goes through (2,2)

  12. Intercepts: Find the intercepts and graph. To find y-intercept: plug in 0 for x To find x-intercept: plug in 0 for y 3rd way Example: y=-x+2 y-intercept: y=-(0)+2 y=2 x-intercept: (0)=-x+2 2=x

  13. Use: y=mx+bory-y1= m(x-x1)b 2.4 Writing equations Slope (m) Slope (m) Point (x1, y1)b y-intercept

  14. Writing equations

  15. Find equation of line given two points (–1, 1) and (2, –5).

  16. You try! Find equation of line given two points (–2, 2) and (2, –4) in point slope form.

  17. Parallel and Perpendicular Lines

  18. Parallel Lines have ___ ___ ____ OUT ___ ___ ____ ______ Slope the same

  19. Perpendicular Lines have _N__ ___ ____ ____ ____ ___ ____ ____ OUT ___ ___ ___ ___ ___ ___ ___ ___ ____ ___ _____ Slope Negative Reciprocals

  20. Parallel and perpendicular lines Perpendicular Parallel Same slope Opposite reciprocal

  21. Parallel Line: Have the same slopes Parallel Line: Perpendicular Line: Have negative reciprocal slopes Perpendicular Line: negative reciprocal

  22. Are the two lines Parallel or Perpendicular? y= mx + b slope Rewrite in y = mx+ b -2x-2x 4y = -2x +9 4 4 4 Parallel Lines

  23. Are the two lines Parallel or Perpendicular? y= mx + b slope Rewrite in y = mx+ b -4-4 X - 4 = -5y -5 -5 -5 Neither Lines

  24. Are the two lines Parallel or Perpendicular? y= mx + b slope Perpendicular Lines

  25. Write the equation of Parallel line in the form y= mx + b Example 1: Write the equation of a line that is parallel to y = -4x + 3 that contains P(1,-2). -4 P(1,-2) Step 1: Find slope and a point Step 1: Step 2: Substitute slope and the point into the point-slope form equation. Step 2: -2 -4 1 Step 3: Rewrite in y = mx + b form. Step 3:

  26. Perpendicular Lines in the form y= mx + b Example 1: Write the equation of a line that is perpendicular to to y = -3x -5 that contains P(-3,7). 3 P(-3,7) Steps1: Find slope and a point Steps1: 1 m= Steps2: Substitute slope and the point into the point-slope form equation. Steps2: 1/3 7 -3 Steps3: Rewrite in y = mx + b form. Steps3:

  27. You try! Example Write the equation of the line in slope-intercept form. parallel to y = 5x – 3 and through (1, 4) m = 5 Parallel lines have equal slopes. Use y – y1 = m(x – x1) with (x1, y1) = (5, 2). y –4 = 5(x – 1) y – 4 = 5x – 5 Distributive property. y= 5x – 1 Simplify.

  28. The slope of the given line is , so the slope of the perpendicular, line is the opposite reciprocal . You try Write the equation of the line in slope-intercept form. perpendicular toand through (0, –2) Use y – y1 = m(x – x1). y + 2 is equivalent to y – (–2). Distributive property. Simplify.

  29. Summarize: In 10 words are less summarize the what you learned. Shared with your group which concept today will most likely appear on the test.

More Related