Chapter 4 Review
Selected Worked Homework Problems
Complete the ordered pairs for each linear equation given:
1.
y=
2
x−3
3
( 0, – 3 )
!
(– 6, – 7 ) !
( 3, – 1 )
!
Given: x = 0
2
y = (0) − 3
3
0
y= −3
!
3
y= 0−3
y = −3
Given: x = −6
2
y = ( −6 ) − 3
3
−12
y=
−3 !
3
y = −4 − 3
y = −7
Given: x = 3
2
y = ( 3) − 3
3
6
y= −3
!
3
y= 2−3
y = −1
( 0,−3)
( −6,−7 )
( 3,−1)
( 6 , 1)
Given: y = 1
2
1= x − 3
3
3 = 2x − 9
12 = 2x
6=x
( 6,1)
3. 3x − 4y = 12 !
( 0 , –3 )
!
( 4 ,0)
Given: x = 0
3( 0 ) − 4y = 12
0 − 4y = 12
−4y = 12
y = −3
( 0,−3 )
Math 100 !
!
!
Given: y = 0
3x − 4(0) = 12
3x − 0 = 12
!
3x = 12
x=4
( 4, 0 )
( 8, 3 )
!
Given: x = 8
3( 8 ) − 4y = 12
24 − 4y = 12
!
−4y = −12
y=3
( 8, 3 )
Chapter 4 Review WKD !
( –4 , – 6 )
Given: y = −6
3x − 4(−6) = 12
3x + 24 = 12
!
3x = −12
x = −4
( − 4, − 6 )
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Find the slope of the line that passes through the given pair of points:
4. (4,5) (−4, 7) !
5. (−3,−2) (2,2)
x1 = 4 y1 = 5 x2 = −4 y2 = 7
m=
7 − (5)
−4 − ( 4 )
m=
7−5
−4 − 4
m=
2
−8
m=
−1
4
!
m=
−4 + 4
−4 − 0
m=
0
−4
m=0
Math 100 !
m=
2 − (−2)
2 − ( −3)
m=
2+2
2+3
m=
4
5
9.
x1 = 0 y1 = −4 x2 = −4 y2 = −4
−4 − (−4)
−4 − ( 0 )
!
x1 = −3 y1 = −2 x2 = 2 y2 = 2
8. (0,−4) (−4,−4) !
m=
!
(8,−8) (8,−4)
x1 = 8 y1 = −8 x2 = 8 y2 = −4
!
m=
−4 − (−8)
8 − (8)
m=
−4 + 8
8−8
m=
4
0
m is undefined
Chapter 4 Review WKD !
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Find the slope and the y-intercept given the equation of the line.
For the equation of the line in the form y = m i x ± b
the number if front of the variable x is the slope
and the constant added or subtracted at the end is the y intercept.
10.
2
x−3 !
3
The number in front of
2
y is the slope
3
y=
11.
!
The constant is the
y intercept − 3
m=
−5x + 3y = 12
−2y = −3x + 8
3y 5x 12
=
+ !
3
3
3
−2y −3x 8
=
+
!
−2
−2 −2
5
x+4
3
m=
y–Intercept = – 3!
3x − 2y = 8
12.
3y = 5x + 12
y=
2
!
3
!
y=
5
!
3
m=
y–Intercept = 4!
14. A line has a slope of
A) The slope of a
line parallel to it = 3
A) The slope of a
line parallel to it =
B) The slope of a line
perpendicular to it =
Math 100 !
−1
3
3
2
y–Intercept = – 4
13. A line has a slope of 3
!
3
x−4
2
−2
5
−2
5
B) The slope of a line
perpendicular to it =
Chapter 4 Review WKD !
5
2
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!
!
Find the equation of line: Write the equation of the line given the following information.
If the slope of the line is NOT equal to 0 or undefined
the equation oft he line is in the form y = mx + b
Substitute the vales for m and B in to y = mx + b
−3
and the
15.
!
2
y − intercept = 4
m=
−3
2
and b = 4
m=
16.
m = −3 and the
!
y − intercept = −1
m = −3
and b = −1
!
!
y = mx + b
−3
y=
x+4
2
17.
y = mx + b
y = −3x − 1
6
and the
!
5
y − intercept = 0
m=
6
5
and b = 0
18.
m = 3 and
passes through (4,2)
m=3 x=4 y=2
m=
y = m(x) + b
y = mx + b
6
y= x
5
!
2 = 3(4) + b
2 = 12 + b
−10 = b
m = 3 and b = −10
y = mix+b
y = 3x − 10
!
Math 100 !
Chapter 4 Review WKD !
© 2016 Eitel
19.
m = −2 and
!
passes through (3,1)
20.
m=0 and
passes through (5,−3)
m = 0 x1 = 5 y1 = −3
m = −2 x = 3 y = 1
A line with a slope of 0
has the equation y = y1
y = m(x) + b
1 = −2(3) + b
y = −3
1 = −6 + b
7=b
!
!!
m = 2 and b = 7
y = mix+b
y = −2x + 7
−1
and
22.
!
4
passes through (−8,6)
2
and
21.
!
3
passes through (6,−3)
m=
m=
m=
2
x = 6 y = −3
3
y = m(x) + b
2
−3 = (6) + b
3
12
−3 = + b
3
−3 = 4 + b
−7 = b
m=
y = m(x) + b
−1
6=
(−8) + b
4
8
6 = +b
4
6 = 2+b
4=b
!
m = 3 and b = −7
m=
y = mix+b
y=
Math 100 !
!
−1
and b = 4
4
y = mix+b
2
x−7
3
!
−1
x = −8 y = 6
4
y=
−1
x+4
4
!
Chapter 4 Review WKD !
© 2016 Eitel
23.
m is undefined and
!
passes through (−2,−6)
25.
m is undefined x1 = −2 y1 = −6
A line with a slope
this is undefined
has the equation x = x1
x = −2
m=
passes through
!
(4, 4) and (−4, 4)
4 − (4)
4−4
0
=
=
−4 − ( 4 ) −4 − 4 −8
m = 0 x1 = −4 y1 = 4
!
A line with a slope of 0
has the equation y = y1
y=4
Math 100 !
Chapter 4 Review WKD !
© 2016 Eitel
Graph each of the following linear equations:
30.
y = 2x − 4
Step 3.
The slope is
Plot ( 0 , – 4 ) !
m=
2
1
!
up 2
right 1
and the y intercept b is – 4
Step 4. go right 1 up 2!
!
Step 5. Draw the graph
and plot a point!
y
y
x
31. y =
Step 3.
−2
x+4
3
The slope is
Plot ( 0 , 4 ) !
m=
−2
3
down 2
right 3
!
through the 2 points!
y
x
x
and the y intercept b is + 4
Step 4. go right 3 down 2!
!
and plot a point
y
through the 2 points!!
y
x
Step 5. Draw the graph
y
x
x
!
!
Math 100 !
Chapter 4 Review WKD !
© 2016 Eitel
34.
x = 2!
35. y = 3
Equations of the form
x = a constant
like
Equations of the form
y = a constant
x=2
like y = 3
!
are graphed as a
horzontial line
through the x axis at 2
!
are graphed as a
horzontial line
through the y axis at 3
y
y
x
x
!
Graph each of the following linear Inequalities:
!
3
3
39. y < x − 3 y is less than but not equal to x − 3
2
2
Step 1!
Step 2
Graph a DASHED line for y =
3
x− 3!
2
Shade the area BELOW the dashed boundary line
y
y
x
Math 100 !
x
Chapter 4 Review WKD !
© 2016 Eitel
40. y ≥
−3
x+4
2
y is greater than or equal to
−3
x+4
2
Step 1!
Step 2
Graph a SOLID line for y =
3
x− 3!
2
Shade the area above the solid boundary line
y
y
x
3x − 4y ≤ 4
46.
x
First solve the inequality for y
−4y ≤ −3x + 4
−4y −3x 4
≤
+
−4
−4 −4
switch the symbol
y≥
3
x −1
4
3
y is greater than or equal to x − 1
4
Step 1!
Step 2
Graph a s SOLID line for y ≥
!
y
3
x − 1!
4
Shade the area ABOVE the solid boundary line
y
x
Math 100 !
x
Chapter 4 Review WKD !
© 2016 Eitel