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Math 71

2.5 – The Point-Slope Form of the Equation of a Line

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We can rewrite this to get the _________________________ of the equation of a line:

If we know a ____________ on a line, and the ___________ of the line, we can use point-slope form to get an equation of the line.

Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation:

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We can rewrite this to get the _________________________ of the equation of a line:

If we know a ____________ on a line, and the ___________ of the line, we can use point-slope form to get an equation of the line.

Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation:

𝑦− 𝑦1

𝑥−𝑥1

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We can rewrite this to get the _________________________ of the equation of a line:

If we know a ____________ on a line, and the ___________ of the line, we can use point-slope form to get an equation of the line.

Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation:

𝑦− 𝑦1

𝑥−𝑥1

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We can rewrite this to get the _________________________ of the equation of a line:

If we know a ____________ on a line, and the ___________ of the line, we can use point-slope form to get an equation of the line.

Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation:

point-slope form

𝑦− 𝑦1

𝑥−𝑥1

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We can rewrite this to get the _________________________ of the equation of a line:

If we know a ____________ on a line, and the ___________ of the line, we can use point-slope form to get an equation of the line.

Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation:

point-slope form𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)

𝑦− 𝑦1

𝑥−𝑥1

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We can rewrite this to get the _________________________ of the equation of a line:

If we know a ____________ on a line, and the ___________ of the line, we can use point-slope form to get an equation of the line.

Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation:

point-slope form𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)

point

𝑦− 𝑦1

𝑥−𝑥1

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We can rewrite this to get the _________________________ of the equation of a line:

If we know a ____________ on a line, and the ___________ of the line, we can use point-slope form to get an equation of the line.

Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation:

point-slope form𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)

point slope

𝑦− 𝑦1

𝑥−𝑥1

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Ex 1.Write the point-slope form of the equation of the line with slope 3 that passes through the point Now write the equation in slope-intercept form. Ex 2.A line passes through the points and . Find an equation of the line in point-slope form.

Now write the equation in slope-intercept form.

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Nonintersecting lines that lie in the same plane are called __________________________.

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Nonintersecting lines that lie in the same plane are called __________________________.parallel lines

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What can you say about the slopes of parallel lines?

If two lines have the same slope, are they guaranteed to be parallel?

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What can you say about the slopes of parallel lines?

If two lines have the same slope, are they guaranteed to be parallel?

They’re the same.

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What can you say about the slopes of parallel lines?

If two lines have the same slope, are they guaranteed to be parallel?

They’re the same.

Yes!

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Ex 3.Write an equation of the line passing through and parallel to the line whose equation is . Express the equation in point-slope form.

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Lines that intersect at a right angle () are called __________________________________.

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Lines that intersect at a right angle () are called __________________________________.perpendicular lines

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What is the slope of line m? What is the slope of line n? What happens when you multiply the slopes?

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What is the slope of line m? What is the slope of line n? What happens when you multiply the slopes?

𝟏𝟑

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What is the slope of line m? What is the slope of line n? What happens when you multiply the slopes?

𝟏𝟑3−1

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What is the slope of line m? What is the slope of line n? What happens when you multiply the slopes?

𝟏𝟑3−1=−𝟑

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What is the slope of line m? What is the slope of line n? What happens when you multiply the slopes?

𝟏𝟑3−1=−𝟑

( 13 )(−3 )=−𝟏

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What is the slope of line m? What is the slope of line n? What happens when you multiply the slopes?

𝟏𝟑3−1=−𝟑

( 13 )(−3 )=−𝟏

Slopes of perpendicular linesare negative reciprocals

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In general, product of slopes of two nonvertical perpendicular lines is ________.

In other words, slopes of two nonvertical perpendicular lines are _____________________________.

For example, if a line has slope , then any perpendicular line will have slope ______.

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In general, product of slopes of two nonvertical perpendicular lines is ________.

In other words, slopes of two nonvertical perpendicular lines are _____________________________.

For example, if a line has slope , then any perpendicular line will have slope ______.

−𝟏

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In general, product of slopes of two nonvertical perpendicular lines is ________.

In other words, slopes of two nonvertical perpendicular lines are _____________________________.

For example, if a line has slope , then any perpendicular line will have slope ______.

−𝟏

negative reciprocals

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In general, product of slopes of two nonvertical perpendicular lines is ________.

In other words, slopes of two nonvertical perpendicular lines are _____________________________.

For example, if a line has slope , then any perpendicular line will have slope ______.

−𝟏

negative reciprocals

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Ex 4.Find the slope of any line that is perpendicular to the line whose equation is .

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Ex 5.Write the equation of the line passing through and perpendicular to the line whose equation is . Express the equation in point-slope form and slope-intercept form.

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point-slope form: parallel same slope(also two vertical lines are parallel) perpendicular slopes are negative reciprocals(also, vertical and horizontal lines are perpendicular)

Summary