notes a7 review of linear functions. linear functions slope – ex. given the points (-4, 7) and...
Post on 20-Jan-2016
214 Views
Preview:
TRANSCRIPT
Notes
A7 Review of Linear Functions
Linear Functions
Slope –
Ex. Given the points (-4, 7) and (-2, -5) find the slope.
Rate of Change
m RunRise
sxinchangesyinchange''
xy
12
12
xxyy
Linear Functions
Slope –
Ex. Given the points (-4, 7) and (-2, -5) find the slope.
Rate of Change
m RunRise
sxinchangesyinchange''
xy
12
12
xxyy
67 54 2
a) Find the slope of the line passing through the given points:
3 5, 2 , , 3
4 4
b) Fine the value of k so that the line through the given points has the given slope:(2, -3) and (k, 7); m = -2
a) Find the slope of the line passing through the given points:
3 5, 2 , , 3
4 4
b) Fine the value of k so that the line through the given points has the given slope:(2, -3) and (k, 7); m = -2
12
3 25 34 4
3
7 3 2k 2 1
Slope-intercept form of a Line: y = mx + bEx. Graph: y = 3x – 2
Vertical Lines: Graph: x = 3 Slope of vertical line:
Horizontal Lines: Graph y = -2 Slope of horizontal line:
Slope-intercept form of a Line: y = mx + bEx. Graph: y = 3x – 2
Vertical Lines: Graph: x = 3 Slope of vertical line:
Horizontal Lines: Graph y = -2 Slope of horizontal line:
UNDEFINED
ZERO (0)
Parallel Lines have the same slope: m1 = m2
Perpendicular Lines have slopes that are negative reciprocals:
12
1m
m
Tell whether the lines are parallel, perpendicular, or neither:
a) Line 1: through (-2, 2) and (0, -1)
Line 2: through (-4,-1) and (2, 3)
Tell whether the lines are parallel, perpendicular, or neither:
a) Line 1: through (-2, 2) and (0, -1)
Line 2: through (-4,-1) and (2, 3)
32
23
PERPENDICULAR
Tell whether the lines are parallel, perpendicular, or neither:
b) Line 1: through (-4, -2) and (1, 7)
Line 2: through (-1,-4) and (3, 5)
Tell whether the lines are parallel, perpendicular, or neither:
b) Line 1: through (-4, -2) and (1, 7)
Line 2: through (-1,-4) and (3, 5)
95
94
NEITHER
Tell whether the lines are parallel, perpendicular, or neither:
c) Line 1: through (1, 2) and (4, -3)
Line 2: through (-4, 3) and (-1, -2)
Tell whether the lines are parallel, perpendicular, or neither:
c) Line 1: through (1, 2) and (4, -3)
Line 2: through (-4, 3) and (-1, -2)
53
53
PARALLEL
Point-Slope Form of a Line: y – y1 = m (x – x1)
Ex. Find the equation of a line in point slope form that passes through the points (4, -2) and (1, 3).
Point-Slope Form of a Line: y – y1 = m (x – x1)
Ex. Find the equation of a line in point slope form that passes through the points (4, -2) and (1, 3).
5m
3
5y 2 x 4
3( ) or
5y 3 x 1
3 ( )
Graph:5
y 2 x 43( )
Graph:5
y 2 x 43( )
Standard Form of a Line: Ax +By = C
where A, B, and C are all relatively prime integers, A > 0
Ex. Transform the previous equation to Standard Form
POSITIVE!!!
5y 2 x 4
3( )
Standard Form of a Line: Ax +By = C
where A, B, and C are all relatively prime integers, A > 0
Ex. Transform the previous equation to Standard Form
POSITIVE!!!
5y 2 x 4
3( )
5x + 3y = 14
Notes
A8Forms of Linear Equations
Parallel Lines:
Ex. Find the equation of a line in slope-intercept form that passes through (-3, 4) and is parallel to
1y x 5
3
Parallel Lines:
Ex. Find the equation of a line in slope-intercept form that passes through (-3, 4) and is parallel to
Point-slope form:
Slope-intercept form:
1y x 5
3
Parallel Lines:
Ex. Find the equation of a line in slope-intercept form that passes through (-3, 4) and is parallel to
Point-slope form:
Slope-intercept form:
1y x 5
3
1y 4 (x 3)
3
Parallel Lines:
Ex. Find the equation of a line in slope-intercept form that passes through (-3, 4) and is parallel to
Point-slope form:
Slope-intercept form:
1y x 5
3
1y 4 (x 3)
3
1y x 5
3
Perpendicular Lines:
Ex. Find the equation of a line in slope-intercept form that is perpendicular to 2x + 4y = -8 and goes through the point (-3, 4).
Perpendicular Lines:
Ex. Find the equation of a line in slope-intercept form that is perpendicular to 2x + 4y = -8 and goes through the point (-3, 4).
Slope for new line:
Point-slope form:
Slope-intercept form:
top related