3-3 Slopes of Lines You used the properties of parallel lines to determine congruent angles. Find slopes of lines. Use slope to identify parallel and perpendicular lines.

The Slope-Intercept Equation y = mx + b slope y-intercept Create an equation of a line with a slope of -3 and a y-intercept of 4. y = -3x + 4 y = 4 – 3x 3x = 4 - y -4 = -y – 3x

The Slope-Intercept Equation Example 1 y = mx + b Create an equation of a line with a slope of -3 and a y-intercept of 4. y = -3x + 4

Example 2 y = mx + b 4 = 3 (-2) + b 4 = -6 + b +6 +6 10 = b Write an equation for the line with slope 3 that contains the point (-2,4) y = mx + b solve for b 4 = 3 (-2) + b substitute 4 = -6 + b simplify +6 +6 10 = b y = 3x + 10

Example 2 Write an equation for the line containing the points (1,5) and (2,8).

Example 3 y = mx + b 5 = 3 (1) + b 5 = 3 + b -3 -3 2 = b y = 3x + 2 Write an equation for the line containing the points (1,5) and (2,8). y = mx + b substitute 5 = 3 (1) + b simplify 5 = 3 + b -3 -3 2 = b y = 3x + 2

Find the Slope of a Line C. Find the slope of the line. Substitute (–2, –5) for (x1, y1) and (6, 2) for (x2, y2). Slope formula Substitution Simplify. Answer:

D. Find the slope of the line. Substitute (–2, –1) for (x1, y1) and (6, –1) for (x2, y2). Slope formula Substitution Simplify. Answer: 0

D. Find the slope of the line. A. 0 B. undefined C. 3 D.

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RECREATION In 2000, the annual sales for one manufacturer of camping equipment was $48.9 million. In 2005, the annual sales were $85.9 million. If sales increase at the same rate, what will be the total sales in 2015? Understand Use the data given to graph the line that models the annual sales y as a function of the years x since 2000. The sales increase is constant. Plot the points (0, 48.9) and (5, 85.9) and draw a line through them. You want to find the sales in 2015.

Plan Find the slope of the line. Use this rate of change to find the amount of sales in 2015. Solve Use the slope formula to find the slope of the line. The sales increased at an average of $7.4 million per year.

Use the slope of the line and one known point on the line to calculate the sales y when the years x since 2000 is 15. Slope formula m = 7.4, x1 = 0, y1 = 48.9, x2 = 15 Simplify. Multiply each side by 15. Add 48.9 to each side. Answer: Thus, the sales in 2015 will be about $159.9 million.

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Parallel Lines Parallel lines are lines in the same plane that never intersect. Parallel lines have the same slope. -8 -6 -4 -2 2 4 6 8

Perpendicular Lines Perpendicular lines are lines that intersect to form a 900 angle. -8 -6 -4 -2 2 4 6 8 The product of the slopes of perpendicular lines is -1.

Determine whether these lines are perpendicular. and y = -3x - 2 m = -3 Since the product of the slopes is -1, the lines are perpendicular.

Determine whether and are parallel, perpendicular, or neither for F(1, –3), G(–2, –1), H(5, 0), and J(6, 3). Graph each line to verify your answer. Step 1 Find the slopes of and . Step 2 Determine the relationship, if any, between the lines. The slopes are not the same, so and are not parallel. The product of the slopes is So, and are not perpendicular.

3-3 Assignment p. 193, 12-38 even, skip 26