4 ~ manale mourdi ~ chapter 4 outstanding project math
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.
-5x -5x subtract -5x to both sides and would get 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
y= -5x-5 OUTPUT
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
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.
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
0 4x+4y=-16 plug in 0 in the « x » value.
4y=-16 all that is left is 4y=-16
We have to isolate the y so we divide by 4 on both sides:
It leaves us with : y = -4 , so the y intercept is (0,-4)
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=-16 all that is left is 4x=-16
We have to isolate the « x » so we divide by 4 on both sides:
It leaves us with : x = -4 , so the y intercept is (-4,0).
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!!
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)
Section 4.4 (continued)
0 Step 1: Find the slope of the
line shown :
0 Let (x1,y1)=(-2,0) and
m(slope)=Y2-Y1 Step 2: write
= 9-0 Step 3: plug in
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 !!
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 isn’t 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
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
We’re 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
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.
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
Thanks For Watching !!
You just learned the basics of GRAPHING LINEAR EQUATIONS AND