Linear Functions and Slopes

Question 1

What does the word slope mean?

Answer 1

The measure of steepness.

Question 2

What does the rise of a slope indicate?

Answer 2

The vertical change.

Question 3

What does the run of a slope indicate?

Answer 3

The horizontal change.

Question 4

What is the point-slope form of an equation of a line?

Answer 4

It is an equation, derived from the forumula for slope, that is used to find the equation of a straight line graph (linear graph).

Question 5

How does the point-slope form of an equation look?

Answer 5

m(x-x_1) = (y-y_1)

Question 6

What’s the difference betweeb (x, y) and (x_1, y_1)?

Answer 6

x and y are unknown points while x_1 and y_1 are known points.

Question 7

What’s a positive slope?

Answer 7

An increasing slope.

Question 8

What’s a negative slope?

Answer 8

A decreasing slope.

Question 9

What’s a constant slope?

Answer 9

A line who’s slope is 0.

Question 10

Does a horizontal line have a slope?

Answer 10

Yes.

Question 11

What’s the slope of a vertical line.

Answer 11

Undefined.

Question 12

What is the slope if m > 0?

Answer 12

Positive, aka increasing.

Question 13

What is the slope if m < 0?

Answer 13

Negative, aka decreasing.

Question 14

What is the slope if m = 0?

Answer 14

Constant, aka zero slope, aka horizontal line.

Question 15

What is the slope if m is undefined?

Answer 15

Undefined slope.

Question 16

What information is needed for finding the equation of a linear graph using the point-slope form?

Answer 16

The slope and a point on the line graph.

Question 17

When is the point-slope form used?

Answer 17

When the slope and an arbitrary point on the line graph are available.

Question 18

What is the slope-intercept form of the equation of a line?

Answer 18

y = mx + b, where m is the slope and b is the intercept.

Question 19

When is the slope-intercept form used?

Answer 19

When the slope and a point, that passes through the graph, which is a y-intercept, are available.

Question 20

How does the slope-intercept form look like in function notation?

Answer 20

f(x) = mx + b.

Question 21

How do we obtain a graph using the slope-intercept form?

Answer 21

1. plot the y-intercept point
2. using the slope, count the vertical change and the corresponding horizontal change and plot a point, starting at the y-intercept point
3. using a straightedge draw a line between the two points

Question 22

What does b mean in the slope-intercept form?

Answer 22

The y-coordinate of the y-intercept.

Question 23

What does m mean in the slope-intercept form?

Answer 23

m is the slope.

Question 24

What’s the name of this form of the line of an equation: f(x) = mx + b?

Answer 24

Slope-intercept.

Question 25

What causes the slope-intercept form to turn into y = b?

Answer 25

If m is 0 the term mx is nulified and what’s left is y = b.

Question 26

Can horizontal linear graphs be graphs of functions?

Answer 26

Yes, they always are.

Question 27

Can vertical linear graphs be graphs of functions?

Answer 27

No.

Question 28

Is this the equation of a line: 3x + 6y = 2?

Answer 28

Yes.

Question 29

In what form is this linear equation: x + 2y = -6

Answer 29

Standard\general.

Question 30

What is a scatter plot, aka. scatter graph?

Answer 30

Data presented in a visual form as a set of points.

Question 31

What is a regression line?

Answer 31

A line that completely fits the data, such that the overall distance from the line to the points outlined on a graph is the smallest.