Download Writing Linear Equations in Point

Writing Linear Equations
in Point-Slope and Standard Form
Chapter 6-2
Point-Slope Form
Point-Slope Form
For a given point (x1, y1) on a nonvertical line
having slope m, the point-slope form of a
linear equation is as follows.
y – y1 = m(x – x1)
Examples
Write the point-slope form of an equation of the line
that passes through the given point and has the
given slope.
1.
(3,5), m = 2
y - y1 = m(x – x1)
y – 5 = 2(x – 3)
2.
(2,9), m = 6
y - y1 = m(x – x1)
y – 9 = 6(x – 2)
More Examples
3.
(-4,7), m = 12
y - y1 = m(x – x1)
y – 7 = 12(x – (-4))
y – 7 = 12(x + 4)
4.
(1,8), m = -10
y - y1 = m(x – x1)
y – 8 = -10(x – 1)
Point-Slope Form
Write the point-slope form of an equation of the
line that passes through the given pair of points.
1.
(2,3), (4,5)
First we must find the slope using the following
m= 5–3
4–2
y2 – y1
x2 – x1
=
2
2
=
1
Now that we know the slope lets plug in point.
y - y1 = m(x – x1)
y – 3 = 1(x – 2) or y – 5 = 1(x – 4)
Point-Slope Form
Write the point-slope form of an equation of the line
that passes through the given pair of points.
2. (2,2), (4,12)
First we must find the slope using the following
m = 12– 2
4–2
y2 – y1
x2 – x1
=
10
2
=
5
Now that we know the slope lets plug in point.
y - y1 = m(x – x1)
y – 2 = 5(x – 2) or y – 12 = 5(x – 4)
Standard Form
Standard Form
Standard Form
The standard form of a linear equation is Ax + By = C,
where A, B, and C are integers, A > 0, and A and B are
not both zero.
Examples
Write the standard form of an equation of the line that
passes through the given point and has the given
slope.
1.(3,5), m = 2
1st
2nd
3rd
4th
5th
6th
y - y1 = m(x – x1)
y – 5 = 2(x – 3)
y – 5 = 2x – 6
y = 2x – 1
-2x + y = -1
2x – y = 1
Point-Slope Form
Use Distributive Property
Add 5 to -6
Subtract 2x
Multiply by (-1)
More Examples
Write the standard form of an equation of the line that
passes through the given point and has the given
slope.
2. (4,7), m = -3
1st
2nd
3rd
4th
5th
y - y1 = m(x – x1)
y – 7 = -3(x – 4)
y – 7 = -3x + 12
y = -3x + 19
3x + y = 19
Point-Slope Form
Use Distributive Property
Add 7 to 12
Add -3x
More Examples
Write the standard form of an equation of the line
that passes through the given pair of points.
3. (2,2), (4,12)
First we must find the slope using the following
m = 12– 2
4–2
y2 – y1
x2 – x1
=
10
2
=
5
Now that we know the slope lets plug in point.
y - y1 = m(x – x1)
y – 2 = 5(x – 2) or y – 12 = 5(x – 4)
#3 Continued
y – 2 = 5(x – 2)
1st
2nd
3rd
4th
5th
or
y – 2 = 5(x – 2)
y – 2 = 5x – 10
y = 5x – 8
-5x + y = -8
5x – y = 8
y – 12 = 5(x – 4)
Point-Slope Form
Use Distributive Property
Add 2 to -10
Subtract 5x
Multiply by (-1)
The End