Holt McDougal Geometry 3-5 Slopes of Lines 3-5 Slopes of Lines Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Geometry

3-5 Slopes of Lines Warm Up Find the value of m undefined0

Holt McDougal Geometry 3-5 Slopes of Lines Warm Up Substitute the given values of m, x, and y into the equation y = mx + b and solve for b. 1. m = 2, x = 3, and y = 0 Solve each equation for y. 3. y – 6x = 9 2. m = –1, x = 5, and y = –4 b = –6 b = x – 2y = 8 y = 6x + 9 y = 2x – 4

Holt McDougal Geometry 3-5 Slopes of Lines Find the slope of a line. Use slopes to identify parallel and perpendicular lines. Objectives

Holt McDougal Geometry 3-5 Slopes of Lines rise run slope Vocabulary

Holt McDougal Geometry 3-5 Slopes of Lines The slope of a line in a coordinate plane is a number that describes the steepness of the line. Any two points on a line can be used to determine the slope.

Holt McDougal Geometry 3-5 Slopes of Lines

Holt McDougal Geometry 3-5 Slopes of Lines Example 1A: Finding the Slope of a Line Use the slope formula to determine the slope of each line. Substitute (–2, 7) for (x 1, y 1 ) and (3, 7) for (x 2, y 2 ) in the slope formula and then simplify. AB

Holt McDougal Geometry 3-5 Slopes of Lines Example 1B: Finding the Slope of a Line Use the slope formula to determine the slope of each line. AC Substitute (–2, 7) for (x 1, y 1 ) and (4, 2) for (x 2, y 2 ) in the slope formula and then simplify.

Holt McDougal Geometry 3-5 Slopes of Lines The slope is undefined. Example 1C: Finding the Slope of a Line Use the slope formula to determine the slope of each line. AD Substitute (–2, 7) for (x 1, y 1 ) and (–2, 1) for (x 2, y 2 ) in the slope formula and then simplify.

Holt McDougal Geometry 3-5 Slopes of Lines A fraction with zero in the denominator is undefined because it is impossible to divide by zero. Remember!

Holt McDougal Geometry 3-5 Slopes of Lines Example 1D: Finding the Slope of a Line Use the slope formula to determine the slope of each line. CD Substitute (4, 2) for (x 1, y 1 ) and (–2, 1) for (x 2, y 2 ) in the slope formula and then simplify.

Holt McDougal Geometry 3-5 Slopes of Lines Check It Out! Example 1 Use the slope formula to determine the slope of JK through J(3, 1) and K(2, –1). Substitute (3, 1) for (x 1, y 1 ) and (2, –1) for (x 2, y 2 ) in the slope formula and then simplify.

Holt McDougal Geometry 3-5 Slopes of Lines One interpretation of slope is a rate of change. If y represents miles traveled and x represents time in hours, the slope gives the rate of change in miles per hour.

Holt McDougal Geometry 3-5 Slopes of Lines Example 2: Transportation Application Justin is driving from home to his college dormitory. At 4:00 p.m., he is 260 miles from home. At 7:00 p.m., he is 455 miles from home. Graph the line that represents Justin’s distance from home at a given time. Find and interpret the slope of the line. Use the points (4, 260) and (7, 455) to graph the line and find the slope.

Holt McDougal Geometry 3-5 Slopes of Lines Example 2 Continued The slope is 65, which means Justin is traveling at an average of 65 miles per hour. Miles Hours

Holt McDougal Geometry 3-5 Slopes of Lines Check It Out! Example 2 What if…? Use the graph below to estimate how far Tony will have traveled by 6:30 P.M. if his average speed stays the same. Since Tony is traveling at an average speed of 60 miles per hour, by 6:30 P.M. Tony would have traveled 390 miles.

Holt McDougal Geometry 3-5 Slopes of Lines Just remember that parallel lines always have the SAME SLOPE and perpendicular line have negative reciprocal slopes.

Holt McDougal Geometry 3-5 Slopes of Lines Example 3A: Determining Whether Lines Are Parallel, Perpendicular, or Neither Graph each pair of lines. Use their slopes to determine whether they are parallel, perpendicular, or neither. UV and XY for U(0, 2), V(–1, –1), X(3, 1), and Y(–3, 3) The products of the slopes is –1, so the lines are perpendicular.

Holt McDougal Geometry 3-5 Slopes of Lines Example 3B: Determining Whether Lines Are Parallel, Perpendicular, or Neither Graph each pair of lines. Use their slopes to determine whether they are parallel, perpendicular, or neither. GH and IJ for G(–3, –2), H(1, 2), I(–2, 4), and J(2, –4) The slopes are not the same, so the lines are not parallel. The product of the slopes is not –1, so the lines are not perpendicular.

Holt McDougal Geometry 3-5 Slopes of Lines Example 3C: Determining Whether Lines Are Parallel, Perpendicular, or Neither Graph each pair of lines. Use their slopes to determine whether they are parallel, perpendicular, or neither. CD and EF for C(–1, –3), D(1, 1), E(–1, 1), and F(0, 3) The lines have the same slope, so they are parallel.

Holt McDougal Geometry 3-5 Slopes of Lines Check It Out! Example 3a Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither. WX and YZ for W(3, 1), X(3, –2), Y(–2, 3), and Z(4, 3) Vertical and horizontal lines are perpendicular.

Holt McDougal Geometry 3-5 Slopes of Lines Check It Out! Example 3b Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither. KL and MN for K(–4, 4), L(–2, –3), M(3, 1), and N(–5, –1) The slopes are not the same, so the lines are not parallel. The product of the slopes is not –1, so the lines are not perpendicular.

Holt McDougal Geometry 3-5 Slopes of Lines Check It Out! Example 3c Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither. BC and DE for B(1, 1), C(3, 5), D(–2, –6), and E(3, 4) The lines have the same slope, so they are parallel.