Download Write an equation of the line.

5.2 Writing Linear Equations Given the Slope
and a Point

Today we will learn how to:
◦ Use slope and any point on a line to write an
equation of the line
◦ Use a linear model to make predictions about a
real-life situation


We already know how to write an equation
given the slope and the y-intercept.
Now we will learn how to write an equation
given its slope and any point on the line.
1. First find the y-intercept.
Substitute the slope m and the coordinates of
the given point (x, y) into the slope-intercept
form, y = mx + b. Then solve for the yintercept b.
2. Then write an equation of the line.
Substitute the slope m and the y-intercept b
into the slope-intercept form y = mx + b.

Example 1
Write an equation of the line that
passes through the point (-3, 0)
and has a slope of 1
3
1. Substitute the slope m and the coordinates
into slope-intercept form:
1
0= 3 (-3) + b
0=-1+ b
1=b
2. Substitute slope m and the y-intercept, b into
the equation:
1
m= 3 , b= 1
y= 1 x + 1
3

Example 2
Write an equation of the line that is parallel to
the line y = -3x – 2 through the point (3, -4).
Find the slope of the line that is parallel to the
line y=-3x-2. So the slope of the line is -3
(when the lines are parallel they have the
same slope)
1. Find the y-intercept
Substitute the slope and the coordinates of the
given point into the equation y=mx+b
-4=-3(3) + b
-4=-9 + b
5=b
2. Write an equation of the line
m=-3, b=5
y=-3x + 5

Writing and Using a Linear Model
VACATION TRIPS Between 1985 and 1995, the
number of vacation trips in the United States
taken by United States residents increased by
about 26 million per year. In 1993, United
States residents went on 740 million vacation
trips within the United States.
a. Write a linear equation that models the number of
vacation trips y (in millions) in terms of the year t.
Let t be the number of years since 1985.
b. Estimate the number of vacation trips in the year
2005
SOLUTION
 a. The number of trips increased by about 26
million per year, so you know the slope is m = 26.
You also know that (t, y) = (8, 740) is a point on
the line, because 740 million trips were taken in
1993, 8 years after 1985.
 y = mt + b
Write slope-intercept form.
 740 = (26)(8) + b
Substitute 26 for m, 8 for t,
and 740 for y.
 740 = 208 + b
Simplify.
 532 = b
The y-intercept is b = 532.
 Write an equation of the line using m = 26 and
b = 532.
 y = mt + b
Write slope-intercept form.
 y = 26t + 532
Substitute 26 for m and 532 forb.







Solution
b. You can estimate the number of vacation
trips in the year 2005 by substituting t = 20
into the linear model.
y = 26t + 532
Write linear model.
= 26(20) + 532
Substitute 20 for t.
= 1052
Simplify.
You can estimate that United States residents
will take about 1052 million vacation trips in
the year 2005.
HOMEWORK
Ch 5.1 w/s
5.3 – Writing Linear Equations Given Two
Points

Today we will learn how to:
◦ Write an equation of a line given two points on the
line



So far in this chapter, we were always
given the slope
Now, we will have to first find the slope
Use the formula from Chapter 4
rise y2  y1
m

run x2  x1
Find the slope. Substitute the coordinates of the
two given points into the formula for slope,
1.
y2  y1
m
x2  x1
2.
3.
Find the y-intercept. Substitute the slope m
and the coordinates of one of the points into
the slope-intercept form, y  mx  b , and solve
for the y-intercept, b.
Write an equation of the line. Substitute the
slope m and the y-intercept b into the slopeintercept form, y  mx  b
Write an equation of the line that
passes through the points (1,6) and
(3,-4).
1.
2.
3.
Find the slope
Find the y-intercept
Write the equation of the line
1.
2.
3.
Find the slope of the line.
m= -5
Find the y-intercept
b=11
Write an equation of the line
y=-5x+11
Lines in the same
plane that do not
intersect are
called parallel
lines. Parallel lines
have the same
slope.
Lines that intersect at
right angles are called
perpendicular lines.
The slopes of these
lines are opposite
reciprocals. (Or they
multiply to equal -1)
Opposite reciprocals????
3…..
1
 ...
4
y = 2x + 2
y = 4x - 2
neither
2x + 6y = 1
4x + 12y =3
parallel
1
x2
5
y  5 x  1
y
perpendicular
1
y  x4
2
Ch. 5.3
(Pg. 288-289)
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