3-7 Equations of Lines in the Coordinate Plane

Slope

• The slope m of a line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points.

• If a line contains the points (x1, y1) and (x2, y2), then the slope of the line is:

2 1

2 1

rise

run

y ym

x x

Finding the Slopes of Lines

• What is the slope of line b?

• What is the slope of line d?

• What is the slope of line c?

What is the slope of line a?

Types of Slope

• The slope of a line can be positive, negative, zero, or undefined.– Positive slope means the line rises (from left to right)– Negative slope means the line falls (from left to right)– Zero slope means the line is horizontal– Undefined slope means the line is vertical

Forms of Linear Equations

• If you know the equation of a line, you can graph it.

Slope-intercept form

Point-slope form

Graphing Lines Using Slope-Intercept Form

• What is the graph of ? 2 13

y x

What is an equation of the line…

…with slope – ½ and y-intercept 2?

…through (-1, 4) with slope -3?

Using Two Points to Write an Equation

• What is an equation of the line through points (-2, -1) and (3, 5)?

What is an equation of the line through points (-2, 5) and (4, -4)?

Writing Equations of Horizontal and Vertical Lines

• What are the equations for the horizontal and vertical lines through (2, 4)?

What are the equations for the horizontal and vertical lines through (4, -3)?

3-8 Slopes of Parallel and Perpendicular Lines

Slopes of Parallel Lines

• If two nonvertical lines are parallel, then their slopes are equal.

• If the slopes of two distinct nonvertical lines are equal, then the lines are parallel.

• Any two vertical lines or horizontal lines are parallel.

Line l3 contains A(-13, 6) and B(-1, 2). Line l4 contains C(3, 6) and D(6, 7). Are l3 and l4 parallel?

Writing Equations of Parallel Lines

• What is an equation of the line parallel to y = -3x – 5 that contains (-1, 8)?

Slopes of Perpendicular Lines

• When two lines are perpendicular, their slopes are opposite reciprocals of each other.– In other words, the product of their slopes is -1.

• Any horizontal line is perpendicular to any vertical line, and vice versa.

Line l3 contains A(2, 7) and B(3, -1). Line l4 contains C(-2, 6) and D(8, 7). Are l3 and l4 perpendicular?

Writing Equations of Perpendicular Lines

• What is an equation of the line perpendicular to y = 1/5x + 2 that contains (15, -4)?