Chapter 4: Graphing Linear Equations and Functions OUTSTANDING PROJECT BY MANALE MOURDI pages 272-273

Manale Mourdi

June 1,2013

Period C

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=-50 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.

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)-5y=5-5y=0

0(also called

x intercept)

0(Also

called y intercept)

y=-5(0)-5y=0-5y=-5

-5

1 y=-5(1)-5y=-5-5y=-10

-10

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 tograph a linear function in slope intercept form!!!

(-1,0)

(0,-5)

(-1,-10)

Section 4.3: Graph Using Intercepts page 272 #12

0You 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.

0These two points are the x and y intercepts.0The x-intercept is the x-coordinate of a point where

the graph crosses the x-axis.0The y-intercept is the y-coordinate of a point where

the graph crosses the y-axis.0To 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.

Section 4.3(continued)0Graph the equation 4x+4y=-16 using the two intercepts.0You can find the intercepts using the original standard form linear

equation or by changing into slope intercept form and taking it from there.

0First find the y-intercept first.I will just use the standard form equation.

04x+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 4It leaves us with : y = -4 , so the y intercept is (0,-4)

Section 4.3(continued)0Now, 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.

04x+4y=-16 plug in 0 in the « y » value. 4x+4(0)=-16 4x=-16 all that is left is 4x=-16We have to isolate the « x » so we divide by 4 on both sides: 4x=-16 4 4It leaves us with : x = -4 , so the y intercept is (-4,0).

Section 4.3(continued)0Step 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)

Section 4.4: Compute The Slope page 273 #16

0Slope 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).

0The 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)

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

60 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)

Section 4.5: Graph Using Linear Equations page 273 #18

0Step 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:

0Move 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 +4xWe’re left with : -1y=-4x+3 -1 -1 -1 Divide each side by '-1’0Simplify, the equation is now in slope intercept form : y = 4x-3

Section 4.5 (continued)

0Step 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.

0The slope is -4 or -4 over 1 meaning you go down four and to the right one.

Section 4.5 (continued)0Step 3: Plot the y-intercept

which is (0,-3) .0From the y-intercept use the

slope(-4) to get another point on the line. Draw a line through the points.

0TADA!!! You’re done and now know everything about slope, intercepts, and graphing linear equations!

(0,-3)

(1,-7)

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

FUNCTIONS!!!