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Linear Equations Foldable

Linear Equations Foldable. Carlos Barron Revised by Leck Nhotsoubanh (2014). Materials. Construction Paper (soft colors ) or computer paper Scissors Graph paper Markers (2 Dark colors) Pen or Pencil. Directions.

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Linear Equations Foldable

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  1. Linear Equations Foldable Carlos Barron Revised by LeckNhotsoubanh(2014)

  2. Materials • Construction Paper (soft colors) or computer paper • Scissors • Graph paper • Markers (2 Dark colors) • Pen or Pencil

  3. Directions • Lay your construction horizontally so that we are folding the 17 inches in half. • We want the largest viewing area as possible. • Fold your construction paper in half, vertically down the middle (taco style). • Fold both ends of the construction paper inward so that they meet at the center crease.

  4. Heading • Using a ruler, measure approximately one and a half inches from the top and mark it. • Do the same for the other side. • Cut off the piece from both sides. Do not cut too much. • This will be front of your foldable; your heading will be displayed here.

  5. Linear Equations • Using one of your markers, write “Linear Equations” in the top as your heading. • Measure about 5 inches from the top and mark both sides of the front cover. • Using your scissors, cut to the first crease. DO NOT CUT ALL THE WAY. (cut along the red lines) • The foldable should start taking form. scrap scrap

  6. Linear Equations Graphing (to graph a linear equation) Point & slope Graphically (write equation given graph or 2 points) X & Y intercepts Sections • Close the flaps so that you can see the front of your cover; you should see 4 individual parts. • Using a marker, label each part as follows: • Graphing (to graph a linear equation) • Graphically (write equation given a Graph or 2 points) • Point and Slope (Graph & write an equation given Point & slope) • x & y intercepts (To graph and write equations)

  7. Linear Functions Example 3 with graph Steps for Graphing Example 1 with graph Steps for an equation given slope & point cut in half cut in half Steps for an equation from a Graph or 2 pts Example 2 with graph Steps for finding x & y-intercepts of an equation Example 4 with graph THIS IS HOW YOUR FOLDABLE WILL LOOK WHEN IT IS COMPLETED

  8. Graphing • On the inside behind the title “Graphing,” we will write the steps necessary to graph a line. • We need a slope (m). • We need a y-intercept (b). • Write down the slope-intercept formula and identify its two parts. • To graph we need: • a slope (m) • A y-intercept (b) Slope-intercept formula Y = mx + b

  9. Example 1 • On the inside of the foldable, glue the coordinate plane given to you. • We will be graphing . - write the equation above the graph • Identify your slope (m) and y-intercept (b). - put a dot for the y-intercept - from the dot count up 2 and right 3 put a dot (repeat) - draw a line through the dots

  10. y 7 6 5 4 3 2 1 x 6 5 4 3 2 1 1 2 3 4 5 6 7 1 2 3 4 5 6 Your graph should look like this

  11. Graphically • On the inside behind the title “Graphically,” we will write the steps necessary to write an equation to a line. • We need a slope (m). • We need a y-intercept (b). • Write down the slope formula. • Write the slope-intercept formula • To write the equation we need: • a slope (m) • A y-intercept (b) m = y1– y2 x1– x2 Slope-intercept formula Y = mx + b

  12. Example 2 • On the inside of the foldable, glue the coordinate plane given to you. • Plot the points and draw the line. • Identify your slope (m) – use the formula and y-intercept (b) from the graph. m = -3 – 0m = -¾ b = -3 0 – -4 • Write the equation to the line given the slope and a y-intercept. Y =-¾ x - 3

  13. y 7 6 5 4 3 2 1 x 6 5 4 3 2 1 1 2 3 4 5 6 7 1 2 3 4 5 6 Your graph should look like this Y =-¾ x - 3

  14. Point and Slope • On the inside behind the title “Point and Slope,” we will write the steps • To graph: start with the point, count up and over for the slope. • To write an equation to a line. • We need a slope (m). • We need a y-intercept (b). • You have to find b – you are given m = x = y = so substitute in the slope-intercept form and solve to find b. • Write your answer in slope-intercept form. • To graph we need: • the point • the slope (m) • To write the equation we need: • slope (m) • y-intercept (b)

  15. Example 3 • On the inside of the foldable, copy: Find a linear equation that has a slope of -3 and passes through the point (2,1). • Graph the line • Find the equation • Plug in the values to find b 1 = -3 * 2 + b 1 = -6 + b 1 + 6 = b • Write the equation y = -3x + 7

  16. y 7 6 5 4 3 2 1 x 6 5 4 3 2 1 1 2 3 4 5 6 7 1 2 3 4 5 6 Your graph should look like this y = -3x + 7

  17. X and Y intercepts • On the inside behind the title “x & y intercepts,” we will graph two intercepts. • To find the x-intercept given the equation • To find the y – intercept given the equation To graph: put a dot on the x intercept and a dot on the y intercept then draw a line through the points Let y = 0 and solve for x Let x = 0 and solve for y

  18. Example 4 • On the inside of the foldable: Glue the graph and write the equation 3x-2y=6 above the graph • Draw a dashed line ( ) under the graph • Write the equation 3x - 2y = 6 Let y = 0 and solve • Draw a dashed line ( ) under the x intercept • Write the equation 3x – 2y = 6 Let x = 0 and solve 3x – 2(0) = 6 3x - 0 = 6 x = 6/3 So the x-intercept is (2, 0) 3(0) -2y = 6 0 - 2y = 6 Y = 6/-2 So the y-intercept is (0, -3)

  19. y 7 6 5 4 3 2 1 x 6 5 4 3 2 1 1 2 3 4 5 6 7 1 2 3 4 5 6 Your graph should look like this 3x - 2y = 6

  20. Special Lines Vertical Horizontal Another FoldableSpecial Lines On the back side of your construction paper, we will address horizontal lines and vertical lines. • On the top, write “Special Lines” as your heading. • Recall that your construction paper is folded vertically down the middle. Label the left hand side as “Vertical” and the right hand side as “Horizontal.”

  21. Vertical Lines • On the left hand side of the foldable, draw the line x = 2. • Do we have both variables? Will it cross both axes? • Discuss points on the line {(2,-2),(2,-1),(2,0)…} • Find the slope. What is the y-intercept? Are there any connections between the slope, y-intercept or the graph? Horizontal Lines • On the right hand side of the foldable. Draw the line y=3. • Do we have both variables? Will it cross both axes? • Discuss points on the line {(-4,3),(-2,3),(0,3)…} • Find the slope. Find the y-intercept.

  22. Special Lines Vertical Horizontal Special Lines • Under the vertical and Horizontal lines draw a dashed line • Write PARALLEL on the left and PERPENDICULAR on the right Perpendicular Parallel

  23. Parallel lines • Have the same slope • Find the line parallel to y = 2x - 4 through the point (3, -1) You have the slope (2) you need the new y- intercept. Use m = 2, x = 3, y = -1 and y = mx + b to find the new b Perpendicular lines • Slope is opposite the reciprocal • Find the line perpendicular to y = 2x - 4 thru the point (3, -1) You have the slope (-1/2 ) you need the new y- intercept. Use m = -1/2, x = 3, y = -1 and y = mx + b to find the new b

  24. Now you have a good study guide. You will have a quiz on Tomorrow, you need to know all allall of this information to do well. Thank You.

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