3.5 lines in the coordinate plane chapter 3: parallel and perpendicular lines
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3.5 Lines in the Coordinate Plane
Chapter 3: Parallel and Perpendicular Lines
3.5 Lines in the Coordinate Plane
Slope-Intercept Form: y = mx + b
m: slope
b: y-intercept
(x, y): point
Slope-Intercept Form
Identify the slope and y-intercept for each:
a. y = 3x + 2 b. y = -2x + 5
c. y = ½x – 5 d. y = 3x – ½
e. y = -5x – 4 f. y = 0.2x + 0.7
Graphing Lines in Slope-Intercept Form Graph the line y = 3/4x + 2
m = b =
Graph the line y = x + 2
m = b =
Graph the line y = 3x + 4
m = b =
Graphing Lines in Slope-Intercept Form Graph the line y = -½x – 2
m = b =
Graph the line y = ½x – 1
m = b =
Graph the line y = -5/3 x + 2
m = b =
Standard Form
Ax + By = C
(3x + 2y = 5)
To Graph from Standard Form, find the x- and y- intercepts:
To find the x-intercept, plug in 0 for y.
To find the y-intercept, plug in 0 for x.
Graphing Using Intercepts
Graph 6x + 3y = 12
Find the x-intercept:
Find the y-intercept:
Graphing Using Intercepts
Graph -2x + 4y = -8
Find the x-intercept:
Find the y-intercept:
Transforming to Slope-Intercept Form
Graph 4x – 2y = 9, using slope-intercept form:
Transforming to Slope-Intercept Form
Graph -5x + y = -3, using slope-intercept form:
Write each equation in slope-intercept form and graph the line: y = 2x + 1 y – 1 = x y + 2x =4 8x + 4y = 16 2x + 6y = 6 ¾x – ½y = 1/8
Point-Slope Form
y – y1 = m(x – x1)
(1, 3) and slope 2: (y – 3) = 2(x – 1)
y – y1 = m(x – x1)
Using Point-Slope Form
Write an equation of the line through point
P(-1, 4) with slope 3.
y – y1 = m(x – x1)
y – y1 = m(x – x1)
Using Point-Slope Form
Write an equation of the line through point
P(2, -4) with slope -1.
Write an equation of the line in point-slope form: P(2, 3), slope = 2 I(4, -1), slope = 3 R(-2, -6), slope = -4 A(6, 1), slope = ½ T(-3, 5), slope -1 E(0, 4), slope 1
Writing an Equation of a Line Given Two Points: Write an equation of the line through A(-2,3) and
B(1,-1):
Find the slope:
Use one point and write the equation in point-slope form:
Writing an Equation of a Line Given Two Points: Write an equation of the line through P(5,0) and
Q(7,-3)
Find the slope:
Use one point and write the equation in point-slope form:
Write an equation in point-slope form of the line that contains the given points: D(0,5) E(5,8)
F(6,2) G(2,4)
H(2,6) I(-1,3)
J(-4,4) K(2,10)
L(-1,0) M(-3,-1)
N(8,10) O(-4,2)
Equations of Horizontal and Vertical Lines: A Horizontal Line cuts through the y-axis, so
the equation is y = A Vertical Line cuts through the x-axis, so the
equation is x =
y = 4 x = 3
Equations of Horizontal and Vertical Lines: Write the Equations of the Horizontal and
Vertical line that goes through the point: (3, 2) Horizontal:
Vertical: (4, 7) Horizontal:
Vertical: (2, 6) Horizontal:
Vertical:
Homework
pg 155 1-37all Workbook 3.5 All
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