October 28, 2016
Lesson 4.5
Point-Slope Form
y −y
Since m =
x −x
m(x2 − x1) = y2 − y1 or y − y1 = m(x − x1)
2
1
2
1
We call y − y1 = m(x − x1) the point-slope
form of a linear equation.
If we are given the slope of a line and the coordinates
of any point on the line, we can write its equation
using this form. Sometimes we will change this result
to slope-intercept form to make it easier to graph.
Write the equation of a line with slope -3 passing
through the point (-9, 6) using the point-slope form
of a linear equation. Change the equation to slopeintercept form.
We begin with the given information
and
. Substitute these values
into the point-slope form of the linear equation,
to get
Change this equation to slope-intercept form.
Where does this line cross the y-axis? At (0, -21)
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October 28, 2016
The Standard Form of a linear equation
is Ax + By = C, where A, B, and C are real
numbers. We are going to want A, B, and
C to be integers and A > 0.
Write the equation of the line through the points
(-5, 6) and (-2, 7) in standard form.
a) Find the slope of the line through these points.
b) Write the equation in point-slope form. Notice
that there are two possibilities here.
c) Change the point-slope equation to standard
form, Ax + BY = C, meeting all the requirements
specified at the top of this page.
.
October 28, 2016
October 28, 2016
Write the required equations for the line below.
•
(4, 4)
(-2, -1)
•
a) Begin by writing a point-slope form equation.
b) Convert point-slope to slope-intercept form.
c) Convert slope-intercept to standard form.
.
October 28, 2016
Lines with the same slope and different y-intercepts
are parallel. All vertical lines are parallel.
Find an equation of the line through the point
(-3, 7) and parallel to the graph of 2x - 4y = 9.
Find the slope of the line 2x - 4y = 9.
Perpendicular lines have slope that are opposite
reciprocals. Horizontal and vertical lines are
perpendicular.
Determine whether the graphs of the lines
5x - 2y = 8 and 2x + 5y = 4 are perpendicular.
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October 28, 2016
Find the equation parallel to
and through the point (4, 0).
The slope of the parallel line is the same as the
given line.
Use the given point, (4, 0), to write a point-slope
form equation.
What is slope-intercept form?
Graph each line in the same window.
Window:
.
October 28, 2016
Find the equation of the line with m = -3
and passing through the point (5, -6). Write
the equation in point-slope form and then
solve it for y. Use your calculator to graph
the equation.
Point-slope form:
Solved for y:
Note that we do not have to simplify the right side of
our equation. The calculator will do it for us.
Window: [-13.2 13.2] [-5.2, 11.2]
What is the x-intercept? (3,0)
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October 28, 2016
Write an equation of the line with x-intercept
2 and slope of .
What ordered pairs corresponds to an x-intercept
We are given
of 2?
The desired equation is
Change the equation to slope-intercept form
and draw the graph without your calculator.
(0, 3)
•
(2, 0)
•
.
October 28, 2016
October 28, 2016
October 28, 2016
October 28, 2016
Write an equation for each line graphed below.
.