Example: Find the slope of the line through (4, – 3 ) and (2, 2). If we let (x1, y1) = (4, – 3) and (x2, y2) = (2, 2), then Note: If we let (x1, y1) be (2, 2) and (x2, y2) be (4, – 3), then we get the same result.

Example Find the slope of the line through (–2, 1) and (3, 5). Graph the line.

Example Find the slope of the line through (4, -3) and (2, 2). Graph the line.

x y Lines with positive slopes increase from left to right. Positive Slope: m > 0 Negative Slope: m < 0 x y Lines with negative slopes decrease from left to right. I call these “diagonal lines”, Ax + By = C.

Example Find the slope of the line y = 3x + 2. 2 (0, 2) 1 5 (1, 5) y = 3x + 2

Find the slope and y-intercept of the line 2x – 6y = 12. First, we need to solve the linear equation for y. – 6y = – 2x + 12 Subtract 2x from both sides. y = x – 2 Divide both sides by –6. Since the equation is now in the form of y = mx + b, slope is y-intercept is (0, –2)

Example Find the slope and the y-intercept of the line –3x + 2y = 11. Solve the equation for y. The slope of the line is 3/2, y-intercept (0, 11/2).

Equation is y = b

Equation is x = a

Diagonal Lines Ax + By = C y = mx + b x = a a y = b b

Example Determine whether the line 6x + 2y = 9 is parallel to –3x – y = 3. Find the slope of each line. 6x + 2y = 9 – 3x – y = 3 The slopes are the same so the lines are parallel.

Example Determine whether the line x + 3y = –15 is perpendicular to –3x + y = – 1 . Find the slope of each line. x + 3y = – 15 – 3x + y = – 1 The slopes are negative reciprocals so the lines are perpendicular.

Example Becky decided to take a bike ride up a mountain trail Example Becky decided to take a bike ride up a mountain trail. The trail has a vertical rise of 90 feet for every 250 feet of horizontal change. As a percent, what is the grade of the trail? The grade of the trail is given by The grade of the trail is The slope of a line can also be interpreted as the average rate of change. It tells us how fast y is changing with respect to x.