Ch. 8/9/12

Linear Equations

100

What is the slope of the line that passes through ( 8, -3 ) and ( 5, 1 )?

m = - 4/3

200

Write the equation in slope-intercept form

3x - 2y = 6

y = 3/2 x - 3

300

What are the possible solutions to a system of linear equations?

No solutions, one solution, infinitely many solutions

400

What is the slope of a line parallel to the line y = 5x?

What is the slope of a line perpendicular to this line?

parallel: m = 5

perpendicular: m = -1/5

500

Identify the x-intercept and y-intercept for the line

 4x - 12y = 24

x-intercept: ( 6, 0 )

y-intercept: ( 0, -2 )

Angles

100

Find the angle complementary to a 39 degree angle.

Find the angle supplementary to a 39 degree angle.

Complementary: 51 degrees

Supplementary: 141 degrees

200

Find the sum of the interior angles of a octagon.

1080 degrees

300

What four pairs of angles around a transversal are congruent?

alternate interior angles, alternate exterior angles, corresponding angles, vertical angles

400

What is the measure of an interior angle of a regular dodecagon (12-sided polygon)?

150 degrees

500

Find the missing exterior angle measure of a quadrilateral if three of the exterior angles measure 56 degrees, 132 degrees, and 94 degrees.

78 degrees

Triangles

100

Determine if the triangle with the following side lengths is a right triangle: 11, 13, 17

No, 290 is not equal to 289

200

Simplify the radical (root 54). Tell if the number is rational or irrational.

3root6

irrational

300

Draw a right triangle and find the missing side length. Write the length in simplest form.

a = 12, c = 18

b = 6root5

400

In a 45-45-90 triangle, one leg measures 7. What are the other side lengths?

second leg = 7

hypotenuse = 7root2

500

A ramp has a height of 5 ft and a horizontal distance of 60 ft. What is the length of the ramp?

approximately 60.2 ft

Coordinate Plane

100

Find the distance between the points ( 0, 3 ) and ( -2, -1 ).

2root5 (or approx. 4.5 units)

200

How does the point ( 9, 5 ) change when reflected over the x-axis?

How does it change when reflected over the y-axis?

reflection over x-axis: ( 9, -5 )

reflection over y-axis: ( -9, 5 )

300

When graphing a linear inequality, how do you know where the solutions are?

Solutions are in the shaded region. If there is a solid line, points on the line are also solutions. 

400

Does the equation y = 10x represent a direct variation? Why or why not? 

If yes, what is the constant of variation?

Yes, the y-intercept is zero and there is a constant rate of change. 

k = 10

500

How does a dilation with a scale factor of 4 differ from a dilation with a scale factor of 1/4?

When k = 4, the dilated image is four times larger (an enlargement). When k = 1/4, the dilated image is four times smaller (a reduction).