Name ________________________________________ Date __________________ Class__________________
Reteach
LESSON
3-6
Lines in the Coordinate Plane
Slope-Intercept Form
Point-Slope Form
point on the line:
(x1, y1) = (−5, 2)
Write the equation of the line through (0, 1) and (2, 7) in slope-intercept form.
Step 1: Find the slope.
m=
=
y 2 − y1
x2 − x1
Formula for slope
7 −1 6
= =3
2−0 2
Step 2: Find the y-intercept.
y = mx + b
Slope-intercept form
1 = 3(0) + b
Substitute 3 for m, 0 for x, and 1 for y.
1=b
Simplify.
Step 3: Write the equation.
y = mx + b
Slope-intercept form
y = 3x + 1
Substitute 3 for m and 1 for b.
Write the equation of each line in the given form.
1. the line through (4, 2) and (8, 5) in
2. the line through (4, 6) with slope
1
2
slope-intercept form
in point-slope form
_________________________________________
_________________________________________
4. the line with x-intercept −5 and
y-intercept 3 in slope-intercept form
3. the line through (−5, 1) with slope 2
in point-slope form
_________________________________________
5. the line through (8, 0) with slope −
in slope-intercept form
3
4
_________________________________________
6. the line through (1, 7) and (−6, 7)
in point-slope form
_________________________________________
_________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
3-46
Holt McDougal Geometry
Name ________________________________________ Date __________________ Class__________________
LESSON
3-6
Reteach
Lines in the Coordinate Plane continued
You can graph a line from its equation.
2
Consider the equation y = − x + 2.
3
y -intercept = 2
run: go left 3 units
rise: go up 2 units
2
slope = −
3
First plot the y-intercept (0, 2). Use rise 2 and
run −3 to find another point. Draw the line
containing the two points.
Parallel Lines
1
y = x +2
3
y=
Intersecting Lines
y=
1
x−2
2
1
x
3
same slope
different y-intercepts
Coinciding Lines
y =−
2
x +1
3
2x � 3y = 3
same slope
same y-intercept
different slopes
Graph each line.
1
1
x+3
9. y − 2 = ( x + 1)
3
4
Determine whether the lines are parallel, intersect, or coincide.
1
10. y = 2x + 5
11. y = x + 4
3
y = 2x − 1
x − 3y = −12
7. y = x − 2
8. y = −
_________________________________________
12. y = 5x − 2
x + 4y = 8
_________________________________________
________________________________________
13. 5y + 2x = 1
2
y =− x+3
5
________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
3-47
Holt McDougal Geometry
Practice B
1. y − 7 = 0
8
2. y + 5 = − (x − 1)
5
3. y = 7x
1
4. y = − x − 1
2
5.
4. Possible answers: (−3.9, 1.1), (1.5, 3.75);
Actual:
⎛ 6 4 11 12 2 11 ⎞ ⎛ 6 4 11 12 2 11 ⎞
,
,
+
−
⎜⎜ − +
⎟, ⎜ − −
⎟
5
5
5 ⎟⎠ ⎜⎝ 5
5
5
5 ⎟⎠
⎝ 5
6.
Reteach
1. y =
3
x−1
4
3. y − 1 = 2(x + 5)
7. coincide
8. parallel
5. y = −
9. intersect
10. RS: y = −52x + 4500; AS: y = −8x + 3000;
34 days
3
x+6
4
2. y − 6 =
4. y =
1
(x − 4)
2
3
x+3
5
6. y − 7 = 0
7.
Practice C
1. AB is the shortest segment because the
shortest distance between parallel lines is
a segment perpendicular to both lines.
Lines p and q both have a slope of 2.6 =
13
. A segment perpendicular to these
5
5
lines must have a slope of − . AB is
13
the only segment listed that has this
slope.
8.
2. y = −2x + 4 + 5 5 ; y = −2x + 4 − 5 5
3. Possible answers: (−2, 4), (1.5, 2.25);
Actual (−2, 4), (1.5, 2.25)
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A29
Holt McDougal Geometry
9.
3. Both companies total costs would be the
same for 10 T-shirts.
10. parallel
11. coincide
12. intersect
13. parallel
Challenge
4. B
1.
5. H
6. B
Reading Strategies
1. Looking at the equation, you can see the
slope and a point on the line.
2. Looking at the equation, you can see that
m is the slope and b is the y-intercept.
2. slope
3. They are both equations of the line, and
they both use the slope and a point on
the line.
3. (0, 2)
4. To be complete, the definition of the
pencil must include an equation of this
vertical line, such as x = 0.
4. point-slope form
5. y + 2 =
5. a. y = mx − 5 and x = 0
b. y = mx + 8 and x = 0
4
4
(x + 2) or y − 2 = (x − 3)
5
5
6. y = 3x − 2
c. y = mx + b and x = 0
6. a. y = mx − 2m and x = 2
b. y = mx + 3m and x = −3
c. y = mx − am and x = a
7. a. y = mx + (2 − m) and x = 1
b. y = mx + (−3 − 2m) and x = 2
c. y = mx + (d − cm) and x = c
8. y = mx + b, for real numbers m and b
9. x = a, for all real numbers a
x
+ b, for all nonzero real numbers
m
m; real numbers b
10. y = −
Problem Solving
1. x + 2y = 78, x + y = 53
2. color: $28, black: $25
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A30
Holt McDougal Geometry