Download G3-6-Lines in Coordinate Plane

3-6
3-6 Lines
Linesininthe
theCoordinate
CoordinatePlane
Plane
Newton
Holt
Geometry
Holt
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 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.
Gauss
Holt Geometry
3-6 Lines in the Coordinate Plane
Vocabulary
point-slope form
slope-intercept form
Euclid
Holt 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.
Euler
Holt Geometry
3-6 Lines in the Coordinate Plane
Holt Geometry
3-6 Lines in the Coordinate Plane
Remember!
A line with y-intercept b contains the point (0, b).
A line with x-intercept a contains the point (a, 0).
Hilbert
Holt Geometry
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 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
Henri Poincarre
Holt Geometry
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
Use the point (3,-5) to find the
slope.
y – y1 = m(x – x1)
y – 0 = 5 (x – 3)
3
5
y = 3 (x - 3)
Holt Geometry
Point-slope form
5
Substitute
3
0 for y1.
Simplify.
for m, 3 for x1, and
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 Geometry
3-6 Lines in the Coordinate Plane
Example 2A: Graphing Lines
Graph each line.
Riemann
Holt Geometry
3-6 Lines in the Coordinate Plane
Example 2B: Graphing Lines
Graph each line.
y – 3 = –2(x + 4)
Galois
Holt Geometry
3-6 Lines in the Coordinate Plane
rise –2
(–4, 3)
run 1
Holt 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.
Descartes
Holt Geometry
3-6 Lines in the Coordinate Plane
Holt 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
Pascal
Holt Geometry
3-6 Lines in the Coordinate Plane
Example 3B: Classifying Pairs of Lines
Determine whether the lines are parallel,
intersect, or coincide.
Ramanujan
Holt 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 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 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 Geometry