3.5 Slopes of Lines Objectives Find the slope of a line. Use slopes to identify parallel and perpendicular lines.

Materials One person from each group Must have expo red marker bigger one Expo smaller thin Poster paper Ruler Piece of paper towel Dry-erase board with grid

Roles in each Group 1.Recorder (must write neat and big enough to see) 2.Graph- using ruler for straight lines 3.Presenter 4. Overseas everyone on task, contributing to group; Hold up work

What are some things we know about slope of a line? Please write slope big across the top of your poster Write your group number and period at the top corner Select one person to write, one to speak Each person will say at least one thing they know to be recorded

Slope Formula Rise is the difference in the y-values of two points on a line Run is the difference in the x-values of two points on a line Slope of a line is the ratio of the rise to run

Parallel or Perpendicular? Parallel- same slope Perpendicular- opposite reciprocal (slopes have a product of -1) Four given points do not always determine two lines. Graph the lines to make sure the points are not collinear.

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. A line parallel to JK needs a slope of? A line perpendicular to JK needs a slope of?

Group Problems Graph each pair of lines. Use their slopes to determine whether they are parallel, perpendicular, or neither. 1.UV and XY for U(0, 2), V(–1, –1), X(3, 1), and Y(–3, 3) 2.GH and IJ for G(–3, –2), H(1, 2), I(–2, 4), and J(2, –4) 3.CD and EF for C(–1, –3), D(1, 1), E(–1, 1), and F(0, 3) 4.WX and YZ for W(3, 1), X(3, –2), Y(–2, 3), and Z(4, 3) 5.KL and MN for K(–4, 4), L(–2, –3), M(3, 1), and N(–5, –1)

Example 1: 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.

Example 2: 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.

Example 3: 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.

Example 4: Determining Whether Lines Are Parallel, Perpendicular, or Neither 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.

Example 5: Determining Whether Lines Are Parallel, Perpendicular, or Neither 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.