Linear Equations Foldable Carlos Barron Revised by Leck

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 • 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.

• 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 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 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) Linear Equations » Graphically (write equation given a Graphing Point & slope Graph or 2 points) Graphically X & Y » Point and Slope (Graph & write an intercepts equation given Point & slope) » x & y intercepts (To graph and write equations) (to graph a linear equation) (write equation given graph or 2 points)

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

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

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

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

Graphically n On the inside behind the title “Graphically, ” we will write the steps necessary to write an To write the equation to a line. equation we need: ü We need a slope (m). • a slope (m) ü We need a y-intercept (b). n Write down the slope formula. • A y-intercept (b) m = y 1 – y 2 n Write the slope-intercept formula x 1 – x 2 Slope-intercept formula Y = mx + b

Example 2 • On the inside of the foldable, glue the coordinate plane given to you. • Plot the points the line. and draw • 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 y 7 6 5 4 3 Y =-¾ x - 3 2 1 6 5 4 3 2 x 1 1 1 2 3 4 5 6 2 3 4 5 6 7

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

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 = -3 x + 7

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

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

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

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

Another Foldable 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

Vertical Lines l 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 l 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 l Have the same slope l Find the line parallel to y = 2 x - 4 through the have the slope (2) you need point (3, -1) You the new y- intercept. Use m = 2, x = 3, y = -1 and y = mx + b to find the new b Perpendicular lines l Slope is opposite the reciprocal l Find the line perpendicular to y = 2 x - 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. You will have a quiz on Tomorrow, you need to know all all of this information to do well. Thank You.