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4 ~ manale mourdi ~ chapter 4 outstanding project math
- 2. Section 4.2: Graphing Linear Functions page 272 #8 0 This will show you how to graph a linear equations given an equation in y=mx+b format. 0 When 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. 0 Graph the equation: y+5x=-5 0 If a line is not in slope-intercept form, then we must solve for y to get it there. 0 Step 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 Now 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-5 OUTPUT (Y) -1 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 1 y=-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 , youve 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) 0 Graph the equation 4x+4y=-16 using the two intercepts. 0 You can find the intercepts using the original standard form linear equation or by changing into slope intercept form and taking it from there. 0 First find the y-intercept first.I will just use the standard form equation. 0 4x+4y=-16 plug in 0 in the 束 x 損 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. Section 4.3(continued) 0 Now, find the x-intercept.I will just use the method used in the previous problem.It doesnt 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 束 y 損 value. 4x+4(0)=-16 4x=-16 all that is left is 4x=-16 We have to isolate the 束 x 損 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 , youve 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 : 1st point : (X1,Y1) , 2nd point : (X2,Y2). EQUATION is SLOPE = RISE= Y2-Y1 (change in y) RUN X2-X1 (change in x)
- 10. Section 4.4 (continued) 0 Step 1: Find the slope of the line shown : 0 Let (x1,y1)=(-2,0) and (x2,y2)=(4,9) m(slope)=Y2-Y1 Step 2: write X2-X1 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 0 Step 1:Make sure the equation is in slope-intercept form.In this case the equation is : 4x-y=3 The equation isnt in slope intercept form, it is in standard form so we have to rewrite it: 0 Move all terms containing y to the left, all other terms to the right. 0 Add '-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 Were left with : -1y=-4x+3 -1 -1 -1 Divide each side by '-1 0 Simplify, 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 xs 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!!! Youre 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!!!