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4-7 Warm Up Write the slope-intercept form of the equation of the line that passes through the two points. 1. (2, 3), (6, 11) (1, -7), (3, -15) Write an equation of the line in point-slope form that passes through the point and has the given slope. Then rewrite the equation in slope-intercept form. 3. (-1, 1), m = (6, -3), m = Write the equation in standard form of the line that passes through the two points. 5. (5, 8), (3, 2) (-4, -5), (-2, 5)

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**Parallel and Perpendicular Lines**

Math 8H 4-7 Parallel and Perpendicular Lines Algebra Glencoe McGraw-Hill JoAnn Evans

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**Horizontal lines are parallel. Vertical lines are parallel.**

When two lines lie in the same plane but never intersect, they are parallel. x x y y Horizontal lines are parallel. Vertical lines are parallel.

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**Graph these three lines on the same coordinate plane:**

x y Will the lines ever intersect? They appear to be parallel. They won’t intersect.

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**If two non-vertical lines have the same slope, they’re parallel.**

What are the slopes of the 3 lines? If two non-vertical lines have the same slope, they’re parallel. x What about their y-intercepts? y Parallel lines have the same slope, but have different y-intercepts.

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**• • • • • • The two lines are parallel because they have the**

Prove whether the graphs of two equations are parallel lines. y • • • x • • • a b The two lines are parallel because they have the same slope, but have different y-intercepts.

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Write the slope-intercept form of an equation of the line that passes through the point (-2, 5) and is parallel to the graph of the equation y = -4x + 2. What will the slope of the line be if it’s parallel to the line y = -4x + 2? -4 We have a point and a slope, which is enough information to find the equation of the line. Parallel lines have the same slope, but different y-intercepts.

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**What will the slope of the line be if it’s parallel to given line?**

Write the slope-intercept form of an equation of the line that passes through the point (12, 3) and is parallel to the graph of the equation What will the slope of the line be if it’s parallel to given line? Parallel lines have the same slope, but different y-intercepts.

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**Horizontal lines and vertical lines are perpendicular to each other.**

Two lines in a plane are perpendicular if they intersect at right angles (90 degree angles). Horizontal lines and vertical lines are perpendicular to each other. y x

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**Two non vertical lines are perpendicular if and only if**

Do you think these lines are perpendicular? y What is the slope of the green line? What is the slope of the blue line? x Two non vertical lines are perpendicular if and only if the product of their slopes is -1.

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**These two lines are perpendicular:**

The product of their slopes is -1. A graphic check will confirm that the two lines are perpendicular. x

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**OPPOSITE RECIPROCALS. If the product of two numbers is -1, they are**

One-third and three are reciprocals. Their product is one. One-third and negative three are opposite reciprocals (one is positive, the other is negative). Their product is -1. What is the opposite reciprocal of....?

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**To determine if two lines are perpendicular:**

Write each equation in slope intercept form. Multiply the slopes of the two lines together. If the product of the two slopes is -1 (the slopes are opposite reciprocals), then the lines are perpendicular.

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Write the slope-intercept form of an equation of the line that passes through the given point and is perpendicular to the graph of the equation. (-4, 5), y = -4x - 1 What is the opposite reciprocal of the given slope? Use y = mx + b

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Write the slope-intercept form of an equation of the line that passes through the given point and is perpendicular to the graph of the equation. (2, 3), 2x + 10y = 3 Put the equation in slope-intercept form to find the slope. Use y = mx + b

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**Determine whether the pair of lines is **

parallel, perpendicular, or neither. Put the second equation in slope-intercept form so the slopes can be compared. The slopes are opposite reciprocals; the lines are perpendicular.

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**Determine whether each pair of lines is **

parallel, perpendicular, or neither. Neither; the slopes are reciprocals, but they aren’t opposite reciprocals. Parallel; the lines have the same slope but have different y-intercepts.

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Warm up Recall the slope formula:

Warm up Recall the slope formula:

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