2.4 Write Equations Of Lines Examples And Worksheet - Chapter 2, Linear Equations And Functions Page 2
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1
2
3
4
5
6
7
8
9E
2
Write an equation given the slope and a point
X A M P L E
Write an equation of the line that passes through (5, 4) and has a slope of 23.
Solution
Because you know the slope and a point on the line, use point-slope form to write
an equation of the line. Let (x
, y
) 5 (5, 4) and m 5 23.
1
1
SIMPLIFY
y 2
y
5 m(x 2
x
)
Use point-slope form.
1
1
EQUATIONS
y 2
4
5 23(x 2 5)
Substitute for m, x
, and y
.
In this book, equations
1
1
written in point-slope
y 2 4 5 23x 1 15
Distributive property
form will be simplifi ed
y 5 23x 1 19
to slope-intercept form.
Write in slope-intercept form.
E
3
Write equations of parallel or perpendicular lines
X A M P L E
Write an equation of the line that passes through (22, 3) and is (a) parallel to,
and (b) perpendicular to, the line y 5 24x 1 1.
Solution
The given line has a slope of m
5 24. So, a line parallel to it has a slope
a.
1
of m
5 m
5 24. You know the slope and a point on the line, so use the
2
1
point-slope form with (x
, y
) 5 (22, 3) to write an equation of the line.
1
1
y 2
y
5
m
(x 2
x
)
Use point-slope form.
1
2
1
y 2
3
5 24(x 2 (22))
Substitute for m
, x
, and y
.
2
1
1
y 2 3 5 24(x 1 2)
Simplify.
y 2 3 5 24x 2 8
Distributive property
y 5 24x 2 5
Write in slope-intercept form.
A line perpendicular to a line with slope m
5 24 has a slope
b.
1
1
1
of m
. Use point-slope form with (x
, y
) 5 (22, 3).
5 2
5
}
}
m
2
1
1
4
1
y 2
y
m
(x 2
x
)
Use point-slope form.
5
1
2
1
1
y 2
3
(x 2 (22))
5
Substitute for m
, x
, and y
.
}
2
1
1
4
1
y 2 3 5
(x 1 2)
Simplify.
}
4
1
1
y 2 3 5
x 1
Distributive property
}
}
4
2
7
1
y 5
x 1
Write in slope-intercept form.
}
}
4
2
✓
G
P
for Examples 2 and 3
UIDED
RACTICE
Write an equation of the line that passes through (21, 6) and has a slope of 4.
4.
Write an equation of the line that passes through (4, 22) and is (a) parallel
5.
to, and (b) perpendicular to, the line y 5 3x 2 1.
99
2.4 Write Equations of Lines
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