Worksheet 3-4 P. 2

DATE

NAME

3-4 Finding an Equation of a Line (continued) Vocabulary j>-intercept The y-coordinate of the point where a line (or curve) intersects the y-axis. x-intercept The ^-coordinate of the point where a line (or curve) intersects the *-axis. Slope-intercept form The equation of a line written as y = mx + b where m is the slope and b is the y-intercept. Theorem Let Zq and L2 be two different lines, with slopes mj and m2. 1. LI and L2 are parallel if and only if m\ = wt2. 2. LI and L2 are perpendicular if and only if mjW 2 = — 1. (mi and ra2 are negative reciprocals.) Example J3

Find an equation in standard form of the line having slope - — and ^-intercept 2.

Solution

Use

= mx + b with m =

y = 3x

--

+ 2

and b = 2. Multiply both sides by 4 to clear the fraction.

4y = -3* + 8 4y = 8

Find an equation in standard form of the line having slope m and ^-intercept b. 17.m=-l,b =

18. /» = 2, b =

-4

19.

20. m = 0.8, & = 0.6

Example 4

Find equations in standard form of the lines through point P( — 1, 3) that are (a) parallel to and (b) perpendicular to the line x - 3y = 6.

Solution

Solve the equation for y to find the slope:

x - 3y = 6; y = ~x - 2 a. A line parallel to x — 3y = 6

.". the slope of the line is —. b. The slope of a line perpendicular to

has the same slope, —-.

x — 3y = 6 is the negative reciprocal

Use the point-slope form:

of —, or —3. Use the point-slope form:

y - 3 =

+ 1)

3v - 9 = x + 1 x - 3y = -10

y - 3 = -3(jc + 1) y - 3 = -3x - 3 3* + y = 0

Find equations in standard form of the lines through point P that are (a) parallel to and (b) perpendicular to line L. 21. P(0, -5);L:y = ~x + 2

22. P(3, 0);L:x -4y = 4

23. P(2, -3);L: 2x + 7y = 14

24. P(-5, -1);L:* + 4 = 0

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Study Guide, ALGEBRA AND TRIGONOMETRY, Structure and Method, Book 2 Copyright © by Houghton Mifflin Company. All rights reserved.