Slopes of lines

Section 1-2: Slopes of Lines

Demo: Slope (Utah State University) Demo: Slope - Intercept Form (Utah State University) Demo: Point-Slope Form (Utah State University)

As you recall from basic algebra, the slope of a non-vertical line measures the steepness of the line as related to the x-axis. If two points are on the same line then the definition of slope is as follows:

Important facts about slope!!

1) Horizontal lines have a slope = 0.

2) Vertical lines have undefined slope because the denominator is zero.

Demo: affect of Slope on a line

Sample graphs of slope!

Note: The blue line has a positive slope because it goes uphill from left to right. The red line has a negative slope because it goes downhill from left to right. The purple line has an undefined slope because it is vertical. The green line has zero as the slope because it is horizontal.

Important facts about slope to remember!

1) The slope of y = mx + b is m. m is always constant for a line.

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

3) Two lines are perpendicular if and only if their slopes are negative reciprocals.

Sample problems

1) Find the slope of the line thru (4,3) and (5,7).

Solution: m = (7 - 3)/(5 - 4) = 4/1 = 4 Make sure you subtract in the same order.

2) Find the slope of the line thru (4,5), (4,3).

Solution: m = (5 - 3)/(4 - 4) = 2/0 = undefined. The line is vertical

3) Find the slope of the line with the equation y = 4x + 5

Solution: It is in the correct form so the slope is m = 4

4) Find the slope of the line with the equation 4x + 2y = 8

Solution: The equation needs to be placed in the correct form.

2y = -4x + 8

y = -2x + 4

Therefore, the slope m = -2. The line is going downhill.

5) y = 4x + 7, y = 4x - 3, y = (-1/4)x + 8. Tell which are parallel and which are perpendicular.

Solution: The first and second are parallel because they have the same slope, while the third equation is perpendicular to the first two because the slope is a negative reciprocal.