Parallel lines
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y. x. Parallel Lines. Two nonvertical lines are parallel if and only if they have the same slope. Parallel lines are two straight lines that never touch. m 1 = m 2. Slope m 1. Parallel lines have the same slope, but different y-intercepts. Slope m 2. Parallel Lines. Slope of Line 1.

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Parallel Lines

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Parallel lines

y

x

Parallel Lines

  • Two nonvertical lines are parallel if and only if they have the same slope.

Parallel lines are two straight lines that never touch.

m1 =m2

Slope m1

Parallel lines have the same slope, but different y-intercepts

Slope m2


Parallel lines

Parallel Lines

Slope of Line 1

Slope of Line 2


Parallel lines1

y

x

Line d has a slope of

Parallel Lines

Example:

Line c has a slope of

If line d is parallel to line c, what is its slope?

Parallel lines have the same slope.

line c

line d


Parallel lines

Write the Equation of a line given a Parallel Line and a Point

Write an equation of a line that is parallel to the line y = x + 8 and passes through the point (– 6, 4)

1

2


Parallel lines

y

x

Write the Equation of a line given a Parallel Line and a Point

Write an equation of a line that is parallel to the line y = x + 8 and passes through the point (– 6, 4)

1

2

Answer: y = x + 7

1

2


Parallel lines

Write the Equation of a line given a Parallel Line and a Point

Write an equation of a line that is parallel to the line y = x – 2 and passes through the point (– 2, 1)

2

3


Parallel lines

Write the Equation of a line given a Parallel Line and a Point

Write an equation of a line that is parallel to the line y = – 3 x – 2 and passes through the point (3, – 4)


Parallel lines

Write the Equation of a line given a Parallel Line and a Point

Write an equation of a line that is parallel to the line y = x + 2 and passes through the point (3, – 2)

1

4


Perpendicular lines

y

x

Perpendicular Lines

Perpendicular lines are two lines that meet in a 90° angle.

Perpendicular lines have a slopes that are negative reciprocals of each other.

1

l1

= -

m1

m2

OR

l2

m1 m2 = -1


Parallel lines

Perpendicular Lines

Slope of Line 2

Slope of Line 1


Perpendicular lines1

Perpendicular Lines

  • Give the slope of a line perpendicular to the given line.

    • y = – 4 x +2

    • y = x – 3

    • y = x – 5

1

2


Parallel lines

Write the Equation of a line given a Perpendicular Line and a Point

Write an equation of a line that is perpendicular to the line y = – 4x + 6 and passes through the point (0, 2)


Parallel lines

Write the Equation of a line given a Perpendicular Line and a Point

Write an equation of a line that is Perpendicular to the line y = x + 3 and passes through the point (4, 5)

1

2


Parallel lines

Standard Form

of a Linear Equation

The standard form of a linear equation is

Ax + By = C

where A and B are not both zero


Forms of linear equations

Forms of Linear Equations

  • Slope-Intercept Form: Given the slope m and the y-intercept b, use this equation:

    y = mx + b

  • Standard Form:

  • Ax + By = C

  • where A and B are not both zero


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