Linear Equations Foldable Carlos Barron Revised by Jamie Kujawa (2007) Nkosi Poole (2012)

Materials Construction Paper (soft colors) Scissors Markers (2 Dark colors) Pen or Pencil

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.

Do the same for the other side. Cut off the piece from both sides. 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. Heading

Using your scissors, cut to the first crease. DO NOT CUT ALL THE WAY. 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. The foldable should start taking form. Linear Equations

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) Linear Equations Graphing X & Y intercepts Graphically Pt & slp

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

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

Example 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

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

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 = y2 – y1 x2 – x1 Slope-intercept formula Y = mx + b

Example 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 – 0 m = -¾ b = -3 0 – -4 Write the equation to the line given the slope and a y-intercept. Y =-¾ x - 3

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

Point and Slope To graph we need: the point the slope (m) 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)

Example On the inside of the foldable, copy: Graph the line 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

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

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

Example 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)

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

Special 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.” Special Lines Vertical Horizontal

Horizontal Lines 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.

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

Parallel lines Have the same slope Perpendicular lines 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

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