Objectives Find the slope of a line.

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Objective - To find the slope of a line.

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Presentation transcript:

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

Vocabulary rise run slope

The ______________________ of a line in a coordinate plane is a number that describes the steepness of the line. Any ________ points on a line can be used to determine the slope.

One interpretation of slope is a rate of change 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.

Example 1A: Finding the Slope of a Line Use the slope formula to determine the slope of each line. AB

Example 1B: Finding the Slope of a Line Use the slope formula to determine the slope of each line. AC

Example 1C: Finding the Slope of a Line Use the slope formula to determine the slope of each line. AD

A fraction with zero in the denominator is undefined because it is impossible to divide by zero. Remember!

Check It Out! Example 1D Use the slope formula to determine the slope of JK through J(3, 1) and K(2, –1).

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.

Check It Out! Example 2B 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.

If a line has a slope of , then the slope of a perpendicular line is . The ratios and are called ________________.

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)

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)

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)