Point-Slope FormulaPoint-Slope Formula

Writing an Equation of a line Using the Point-Slope Formula

1 1( )y y m x x

The point-slope formula is given by

where m is the slope of the line and is a known point on the line.

1 1( )y y m x x

1 1( , )x y

Writing an Equation of a Line Using the Point-Slope Formula

m = 3Point ( -2, -4 )

The point-slope formula: 1 1( )y y m x x -4 3

-2 -4

3

-2

Simplify. Because the final answer is required in slope-intercept form, simplify the equation and solve for y.

y + 4 = 3(x + 2)

Apply the distributive property y + 4 = 3x + 6

Subtract 4 from both sides. y + 4 – 4 = 3x + 6 -4

Slope-intercept formy = 3x +2

2 1

2 1

y ym

x x

Writing an Equation of a Line Through Two Points

Points (-2, 5) and (4, -1)

The point-slope formula: 1 1( )y y m x x 5 -1

-1

4

5

-2

Simplify. Because the final answer is required in slope-intercept form, simplify the equation and solve for y.

y – 5 = -1(x – (-2)

Apply the distributive property y - 5 = -x + 2

Add 5 to both sides. y -5 + 5 = -x + 2 +5

Slope-intercept formy = -x + 3

Find the slope

-2 5-14

-2

61

6m

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)

1 1( )y y m x x -1-40

y = -4( x +1)y = -4x -4

Lets use the graph to find the equation.What is the slope and the y-intercept?

What formula could we use to write the equation?

Slope-intercept formy = mx + b

m = -4b = -4

y = mx + by = -4x -4

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.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

1 1( )y y m x x (-3)1 ⅓Point-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.

y – 1 = ⅓(x + 3)

Apply the distributive propertyy - 1 = ⅓x + 1

Add 1 to both sidesy = ⅓x + 2

Form Equation CommentsStandard form

Ax + By = C4x + 2y = 8 A and B must not both be zero

Horizontal Liney = k (k is a constant)

y = 4 The slope is zero and the y-intercept is (0, k).

Vertical linex = h (h is a constant)

x = -1 The slope is undefined, and the x-intercept is (h, 0)

Slope-intercept Formy = mx + b

The slope is m y-intercept is (0, b)

y = -3x +7Slope = -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 y-intercept.

Point-Slope Formulay - 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

Different forms of Linear Equations: