1. C h a p t e r 4 : G r a p h i n g L i n e a r E q u a t i o n s a n d F u n c t i o n s O U T S T A N D I N G P R O J E C T B Y M A N A L E M O U R D I p a g e s 2 7 2 - 2 7 3 Manale Mourdi June 1,2013 Period C

2. Section 4.2: Graphing Linear Functions page 272 #8 0T0T his will show you how to graph a linear equations given an equation in y=mx+b format. 0W0W hen an equation is in slope-intercept form the “y” is always on one side by itself. There can not be more than one y either. 0G0G raph the equation: y+5x=-5 0I0I f a line is not in slope-intercept form, then we must solve for “y” to get it there. 0S0S tep 1: Solve the equation for y.You have to isolate the variable y. 0 y +5x=-5 -5x -5x subtract -5x to both sides and would get y =-5x-5 y= -5x-5 0 N ow the equation is in y=mx+b format: m is the slope which is -5, and b is the second fixed constant to appear in an algebraic equation in this case is 5.

3. Section 4.2 (continued) 0 Step 2: Make a table,choose a few values for x. For now I will include three values in the table : A negative number, zero, and a positive number. Then, calculate the y values. 0 For my x values I will choose -1, 0,and 1. 0 The y values I found were 0, -5 and -10. INPUT (X) y= -5x-5OUTPUT (Y) y=-5(-1)-5 y=5-5 y=0 0 (also called x intercept) 0 (Also called y intercept) y=-5(0)-5 y=0-5 y=-5 -5 1y=-5(1)-5 y=-5-5 y=-10 -10

4. Section 4.2(continued) 0 Step 3:Plot the points on a graph made to scale. In this case I will use a scale by twos. By making a table it gives me three points, in this case (- 1, 0) (0, -5) and (1, -10) to plot and draw the line. Remember when plotting points you always start at the origin. Next you go left (if x- coordinate is negative) or right (if x-coordinate is positive. Then you go up (if y-coordinate is positive) or down (if y-coordinate is negative) Step 4: Connect the points by drawing a line through Make sure your line covers the graph and has arrows on both ends. Be sure to use a ruler.. Label the points too. Step 5: Go take a break, you’ve just learned how to graph a linear function in slope intercept form!!! (-1,0) (0,-5) (-1,-10)

5. Section 4.3: Graph Using Intercepts page 272 #12 0 You can use the fact that two points determine a line to graph a linear equation. Two convenient points are the points where the graph crosses the axes. 0 These two points are the x and y intercepts. 0 The x-intercept is the x-coordinate of a point where the graph crosses the x-axis. 0 The y-intercept is the y-coordinate of a point where the graph crosses the y-axis. 0 To find the x-intercept of the graph of a linear equation, find the value of x when y=0. To find the y- intercept of the graph, find the value of y when x=0.

6. Section 4.3(continued) 0G0G raph the equation 4x+4y=-16 using the two intercepts. 0Y0Y ou can find the intercepts using the original standard form linear equation or by changing into slope intercept form and taking it from there. 0F0F irst find the y-intercept first.I will just use the standard form equation. 0404 x+4y=-16 plug in 0 in the « x » value. 4(0)+4y=-16 4y=-16 all that is left is 4y=-16 We have to isolate the y so we divide by 4 on both sides: 4y=-16 4 4 It leaves us with : y = -4, so the y intercept is (0,-4)

7. 0 Now, find the x-intercept.I will just use the method used in the previous problem.It doesn’t matter what order you find the intercepts or what method you choose because the answer remains the same. 0 4x+4y=-16 plug in 0 in the « y » value. 4x+4(0)=-16 4x=-16 all that is left is 4x=-16 We have to isolate the « x » so we divide by 4 on both sides: 4x=-16 4 4 It leaves us with : x = -4, so the y intercept is (-4,0).

8. Section 4.3(continued) 0 Step 2 : Plot the points that correspond to the intercepts: y- intercept is (0,-4) and y intercept is (-4,0). Step 3: Connect the points by drawing a line t through them. Make sure your line covers the graph and has arrows on both ends. Be sure to use a ruler. Step 4: Go take a break, you’ve just learned how to graph using intercepts!! (0,-4) (-4,0)

9. Section 4.4: Compute The Slope page 273 #16 0 Slope is the ratio of the vertical rise to the horizontal run between any two points on a line. Usually referred to as the ratio of the rise(change in y) over run(change in x). 0 The formula for finding slope is used when you know two points of a line. The two points look like : 1 st point : (X 1, Y 1 ), 2 nd point : (X 2,Y 2 ). EQUATION is SLOPE = RISE= Y 2 -Y 1 (change in y) RUN X 2 -X 1 (change in x)

10. Section 4.4 (continued) 0 Step 1: Find the slope of the line shown : 0 Let (x 1,y 1 )=(-2,0) and (x 2,y 2 )=(4,9) m(slope)=Y 2 -Y 1 Step 2: write X 2 -X 1 formula = 9-0 Step 3: plug in 4-(-2) values = 9 6 0 Now the slope is 9/6 meaning we go up 9 and to the right 6 because our slope is positive. 0 The line rises from left to right so the slope is positive. 0 DONE !! (4,9) (-2,0)

11. Section 4.5: Graph Using Linear Equations page 273 #18 0S0S tep 1:Make sure the equation is in slope-intercept form.In this case the equation is : 4x-y=3 The equation isn’t in slope intercept form, it is in standard form so we have to rewrite it: 0M0M ove all terms containing y to the left, all other terms to the right. 0 A dd '-4x' to each side of the equation to leave -1y alone. Notice that I added a -1 to the –y because we will need to get rid of the negative later on. -4x + -1y = 3 +4x +4x We’re left with : -1y=-4x+3 -1 -1 -1 Divide each side by '-1’ 0S0S implify, the equation is now in slope intercept form : y = 4x-3

12. Section 4.5 (continued) 0 Step 2 : Identify the slope and y-intercept. Since the equation is y = 4x-3, we can easily identify the y intercept which is in this case (0,-3) because when you plug in 0 to the x’s spot, y= -3.Instead of doing all this work just look at b which is the second fixed constant to appear in this equation. 0 The slope is -4 or -4 over 1 meaning you go down four and to the right one.

13. Section 4.5 (continued) 0 Step 3: Plot the y-intercept which is (0,-3). 0 From the y-intercept use the slope(-4) to get another point on the line. Draw a line through the points. 0 TADA!!! You’re done and now know everything about slope, intercepts, and graphing linear equations! (0,-3) (1,-7)

14. Thanks For Watching !! You just learned the basics of GRAPHING LINEAR EQUATIONS AND FUNCTIONS!!!