Transcript Point-Slope Formula

Point-Slope Formula
y  y1  m( x  x1 )
Writing an Equation of a line Using
the Point-Slope Formula
The point-slope formula is given by
y  y1  m( x  x1 )
where m is the slope of the line and
( x1 , y1 ) is a known point on the line.
Writing an Equation of a Line Using the
Point-Slope Formula
m = 33
-2 -4
-4 )
Point ( -2,
The point-slope formula:
3 (x  x
-21 )
y  y-41  m
Simplify. Because the final answer is required in
slope-intercept form, simplify the equation and
solve for y.
Apply the distributive property
Subtract 4 from both sides.
Slope-intercept form
y + 4 = 3(x + 2)
y + 4 = 3x + 6
y + 4 – 4 = 3x + 6 -4
y = 3x +2
Writing an Equation of a Line Through
Two Points
-16
51
y

2  y
mm



1
x
462  x
-2 1
Points (-2,
-1)
-2 5)
5 and (4,
4 -1
Find the slope
The point-slope formula:
-1( x  x
-21 )
y  y51  m
Simplify. Because the final answer is required in
slope-intercept form, simplify the equation and
solve for y.
Apply the distributive property
Add 5 to both sides.
Slope-intercept form
y – 5 = -1(x – (-2)
y - 5 = -x + 2
y -5 + 5 = -x + 2 +5
y = -x + 3
Write an Equation of a Line Parallel to
Another Line
Use the point-slope formula to find an equation of the line
passing through the point(-1, 0) and parallel to the line
y = -4x + 3, Write the final answer in slope-intercept form.
Lets now apply the point-slope
formula using m = -4 point = (-1, 0)
-4 ( x  -1
y  y0 1  m
x1 )
y = -4( x +1)
y = -4x -4
m = -4
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Write an Equation of a Line
Perpendicular to Another Line
Use the point-slope formula to find an equation of the line passing through the point (-3, 1)
and perpendicular to the line 3x + y = -2. Write the final answer in slope-intercept form.
The given line can be written in slope-intercept form as y = -3x -2. The
slope of this line is -3. Therefore, the slope of a line perpendicular to
the given line is ⅓
y  y1 1  ⅓m( x (-3)x1 )
y – 1 = ⅓(x + 3)
y - 1 = ⅓x + 1
Point-slope formula
Substitute m = ⅓ x₁ = -3, y₁ = 1
To write the final answer in slope-intercept
form, simplify the equation and solve for y.
Apply the distributive property
y = ⅓x + 2
Add 1 to both sides
Different forms of Linear Equations:
Form
Equation
Comments
Standard form
Ax + By = C
4x + 2y = 8
A and B must not both be zero
Horizontal Line
y = k (k is a constant)
y=4
The slope is zero and the yintercept is (0, k).
Vertical line
x = h (h is a constant)
x = -1
The slope is undefined, and
the x-intercept is (h, 0)
Slope-intercept Form
y = mx + b
The slope is m y-intercept is
(0, b)
y = -3x +7
Slope = -3 y-intercept is (0, 7)
Solving a linear equation for
results in slope-intercept form.
The coefficient of the x-term is
the slope, and the constant
defines the location of the yintercept.
Point-Slope Formula
y - y₁ = m(x - x₁)
m = -3
(x₁, y₁) = (4, 2)
y – 2 = -3(x – 4)
This formula is typically used
to build an equation of a line
when a point on the line is
known and the slope of the
line is known