Analytic Geometry - Review

1) For each of the following pairs of points, solve for i] the distance between the points. ii] the midpoint. iii] the rise. iv] the run. v] the slope. vi] the equation of the line. vii] the slope of a line parallel to the line. viii] the slope of a line perpendicular to the line.

(a) ( l , 2 ) a n d ( 2 , 5 )

(b) ( - 3 , 4 ) a n d ( 3 , - 4 )

(c) ( - 5 , - l ) a n d ( 4 , - 6 )

2) Graph each of the lines in 1.

3) Graph the following linear equations using a table of values.

(a) 3x -y=9 (b) x + 2y=10

4) Graph the following linear equations using double-intercepts. 1 W M^^f^lj

(a) 4x-3y=-12 (b) x + 7y=14

5) Graph the following linear equations using slope-intercept.

(a) y = 4x - 3 (b) 2y - 2 = 4x

6) A line has a slope of -2/5. Generate the coordinates of two points that would lie on the same line.

7) I f the slope of a line is 4 and passes through the points ( - 2 , - 6 ) and (1 , k), what is the value of k?

8) Write the equation of the line and graph the line for each of the following. Leave the answers for (a) and (b) in slope-intercept form and the answers for (c) and (d) in standard form.

(a) m = -1/7 , b = 3

(b) The line has a slope of 1/2 and passes through P( -3 , 4 )

(c) The line passes through F( -5 , 2 ) and G( 3 ,7 )

(d) x-intercept of 4, slope of -3

9) Given the following graphs, determine the equation of the line.

10) State the slope and the y-intercept of the following linear equations.

(a) 3y=-2x + 12 (b) 5x-3y + 7 = 0

11) Determine the equation of the line that passes through ( 4 , 5 ) and is perpendicular to 3x + 4y + 5 = 0.

12) Determine the equation of the line that has an x-intercept of -5 and is parallel to the line -2x + 6y = 9

(a) I] 3.16 ii] ( 1.5 , 3.5 ) iii] 3 iv] 1 v] 3 vi] y = 3x- 1 vii] 3 viii] -1/3

(a) "1 7

3) (a)

4) (a)

5) (a)

20S Pre-Calculus

Analytic Geometry - Review Answer Key

(b) I] 10 © H ii] ( 0 , 0 ) ii] iii] -8 iii] iv] 6 iv] v] -4/3 v] vi] 4x + 3y = 0 vi] vii] -4/3 vii] viii] VA viii]

V\ y1 ©

6) Answers will vary.

8) (a) y = -x/7 + 3 © 5x-8y + 41=0

9) (a) t Z

10) (a) m = -2/3 , b = 4

11) 4x - 3y - 1 = 0

12) .

(b) (d)

(b)

(b)

y = x/2 + 11/2 3x + y- 12 = 0

y = -3x + 6

m = 5/3 , b = 7/3

y 3 ^ -3

10.30 ( -1/2 , -7/2 ) -5 9 -5/9 5x + 9y + 34 -5/9 9/5

The Equation of a Line Review m 1. Find an equation of a line:

a) with a slope of-2 and a y-intercept of-1

b) with a slope of-2 and passing through the point (3,4)

c) passing through the points (5, -2) and (4, 3)

d) that is parallel to y=5x +1 and passes through (2, 5)

e) that is parallel to 4x - 2y + 5 = 0 and passes through (1, -2)

f) that is perpendicular to y = J c -1 and passes through (2, 7) 2

g) that is perpendicular to 2x - y + 2 = 0 and has a y-intercept of -3

h) that is parallel to the x - axis and passes through (0,**2)

^ i) that has a slope of 4 and an x - intercept of 3.

2. What is the equation of a vertical line that passes through the point (2,1)?

3. Given a midpoint M(4, 2) and an endpoint A(1, -2) find the coordinates of the other endpoint B.

4. Given a midpoint M(1, -6) and an endpoint A(4, -5) find the coordinates of the other endpoint B.

The Equation of a Line Review Answer Key

y = mx + b form

a) y = -2x -1

b) y = -2x +10

c) y = -5x +23

d) y = -5x -5

e) y = 2x-4

f) y = -2x +11

g) y = -lx - 3

2

h) y = -2

i) y = 4x -12

Standard form

2x + y + 1 = 0

2x + y-10 = 0

5x + y -23 = 0

5x + y + 5 = 0

2x - y - 4 = 0

2x + y + 11 =0

x + 2y + 6 = 0

y < 2 Lj + 2.

4x - y -12 = 0

2. x = 2

3. (7,6)

4. (-2,-7)