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3-6
3-6 Lines
Linesininthe
theCoordinate
CoordinatePlane
Plane
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Geometry
Holt
McDougal
Geometry
3-6 Lines in the Coordinate Plane
Warm Up
Substitute the given values of m, x, and y into
the equation y = mx + b and solve for b.
1. m = 2, x = 3, and y = 0 b = –6
2. m = –1, x = 5, and y = –4 b = 1
Solve each equation for y.
3. y – 6x = 9
y = 6x + 9
4. 4x – 2y = 8 y = 2x – 4
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
Objectives
Graph lines and write their equations in
slope-intercept and point-slope form.
Classify lines as parallel, intersecting, or
coinciding.
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
Vocabulary
point-slope form
slope-intercept form
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
The equation of a line can be written in
many different forms. The point-slope and
slope-intercept forms of a line are
equivalent. Because the slope of a vertical
line is undefined, these forms cannot be
used to write the equation of a vertical line.
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
Example 2A: Graphing Lines
Graph each line.
The equation is given in the
slope-intercept form, with a
slope of
and a y-intercept
of 1. Plot the point (0, 1) and
then rise 1 and run 2 to find
another point. Draw the line
containing the points.
Holt McDougal Geometry
run 2
rise 1
(0, 1)
3-6 Lines in the Coordinate Plane
Example 2B: Graphing Lines
Graph each line.
y – 3 = –2(x + 4)
The equation is given in the
point-slope form, with a slope
of
through the point (–4, 3).
Plot the point (–4, 3) and then
rise –2 and run 1 to find
another point. Draw the line
containing the points.
Holt McDougal Geometry
rise –2
(–4, 3)
run 1
3-6 Lines in the Coordinate Plane
Example 2C: Graphing Lines
Graph each line.
y = –3
The equation is given in the form
of a horizontal line with a
y-intercept of –3.
The equation tells you that the
y-coordinate of every point on
the line is –3. Draw the
horizontal line through (0, –3).
Holt McDougal Geometry
(0, –3)
3-6 Lines in the Coordinate Plane
Check It Out! Example 2a
Graph each line.
y = 2x – 3
The equation is given in the
slope-intercept form, with a
slope of
and a y-intercept
of –3. Plot the point (0, –3)
and then rise 2 and run 1 to
find another point. Draw the
line containing the points.
Holt McDougal Geometry
run 1
rise 2
(0, –3)
3-6 Lines in the Coordinate Plane
Check It Out! Example 2b
Graph each line.
The equation is given in the
point-slope form, with a slope
rise –2
(–2, 1)
of
through the point (–2, 1).
Plot the point (–2, 1)and then
rise –2 and run 3 to find
another point. Draw the line
containing the points.
Holt McDougal Geometry
run 3
3-6 Lines in the Coordinate Plane
Check It Out! Example 2c
Graph each line.
y = –4
The equation is given in the form
of a horizontal line with a
y-intercept of –4.
The equation tells you that the
y-coordinate of every point on
the line is –4. Draw the
horizontal line through (0, –4).
Holt McDougal Geometry
(0, –4)
3-6 Lines in the Coordinate Plane
Example 1A: Writing Equations In Lines
Write the equation of each line in the given
form.
the line with slope 6 through (3, –4) in pointslope form
y – y1 = m(x – x1)
y – (–4) = 6(x – 3)
Holt McDougal Geometry
Point-slope form
Substitute 6 for m, 3 for
x1, and -4 for y1.
3-6 Lines in the Coordinate Plane
Example 1B: Writing Equations In Lines
Write the equation of each line in the given form.
the line through (–1, 0) and (1, 2) in slopeintercept form
Find the slope.
y=x+1
Holt McDougal Geometry
Write in slope-intercept form using
m = 1 and b = 1.
3-6 Lines in the Coordinate Plane
Example 1C: Writing Equations In Lines
Write the equation of each line in the given form.
the line with the x-intercept 3 and y-intercept
–5 in point slope form
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
Check It Out! Example 1a
Write the equation of each line in the given form.
the line with slope 0 through (4, 6) in slopeintercept form
y – y1 = m(x – x1)
Point-slope form
y – 6 = 0(x – 4)
Substitute 0 for m, 4 for
x1, and 6 for y1.
y=6
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
Check It Out! Example 1b
Write the equation of each line in the given form.
the line through (–3, 2) and (1, 2) in pointslope form
Find the slope.
y – y1 = m(x – x1)
Point-slope form
y – 2 = 0(x – 1)
Substitute 0 for m, 1 for x1, and 2
for y1.
y-2=0
Simplify.
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
A system of two linear equations in two variables
represents two lines. The lines can be parallel,
intersecting, or coinciding. Lines that coincide
are the same line, but the equations may be
written in different forms.
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
Example 3A: Classifying Pairs of Lines
Determine whether the lines are parallel,
intersect, or coincide.
y = 3x + 7, y = –3x – 4
The lines have different slopes, so they intersect.
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
Example 3B: Classifying Pairs of Lines
Determine whether the lines are parallel,
intersect, or coincide.
Solve the second equation for y to find the slopeintercept form.
6y = –2x + 12
Both lines have a slope of
, and the y-intercepts
are different. So the lines are parallel.
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
Example 3C: Classifying Pairs of Lines
Determine whether the lines are parallel,
intersect, or coincide.
2y – 4x = 16, y – 10 = 2(x - 1)
Solve both equations for y to find the slopeintercept form.
2y – 4x = 16
2y = 4x + 16
y = 2x + 8
y – 10 = 2(x – 1)
y – 10 = 2x - 2
y = 2x + 8
Both lines have a slope of 2 and a y-intercept of 8, so
they coincide.
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
Check It Out! Example 3
Determine whether the lines 3x + 5y = 2 and
3x + 6 = -5y are parallel, intersect, or coincide.
Solve both equations for y to find the slopeintercept form.
3x + 5y = 2
3x + 6 = –5y
5y = –3x + 2
Both lines have the same slopes but different
y-intercepts, so the lines are parallel.
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
Lesson Quiz: Part I
Write the equation of each line in the given
form. Then graph each line.
1. the line through (-1, 3)
and (3, -5) in slopeintercept form.
y = –2x + 1
2. the line through (5, –1)
with slope in point-slope
form.
y + 1 = 2 (x – 5)
5
Holt McDougal Geometry
3-6 Lines in the Coordinate Plane
Lesson Quiz: Part II
Determine whether the lines are parallel,
intersect, or coincide.
3. y – 3 = –
1
x, y – 5 = 2(x + 3)
2
intersect
4. 2y = 4x + 12, 4x – 2y = 8
parallel
Holt McDougal Geometry