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) 2. (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 = 4. (6, -3), m = Write the equation in standard form of the line that passes through the two points. 5. (5, 8), (3, 2) 6. (-4, -5), (-2, 5)

Parallel and Perpendicular Lines Math 8H 4-7 Parallel and Perpendicular Lines Algebra 1 Glencoe McGraw-Hill JoAnn Evans

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.

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.

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.

• • • • • • 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.

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.

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.

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

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.

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

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....?

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.

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

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

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.

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.