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

y - y₁ = m(x - x₁).

Question 5

What’s the difference between (x, y) and (x₁, y₁)?

Answer 5

x and y are general variables representing any point’s horizontal and vertical coordinates.
x₁ and y₁ specifically refer to the coordinates of a particular point, often used when multiple points are involved in calculations.

Question 6

What’s a positive slope?

Answer 6

An increasing slope.

Question 7

What’s a negative slope?

Answer 7

A decreasing slope.

Question 8

What’s a constant slope?

Answer 8

A line who’s slope is 0.

Question 9

Does a horizontal line have a slope?

Answer 9

Yes.

Question 10

What’s the slope of a vertical line.

Answer 10

Undefined.

Question 11

What is the slope if m > 0?

Answer 11

Positive, aka increasing.

Question 12

What is the slope if m < 0?

Answer 12

Negative, aka decreasing.

Question 13

What is the slope if m = 0?

Answer 13

Constant, aka zero slope, aka horizontal line.

Question 14

What is the slope if m is undefined?

Answer 14

Undefined slope.

Question 15

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

Answer 15

The slope and a point on the line graph.

Question 16

When is the point-slope form used?

Answer 16

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

Question 17

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

Answer 17

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

Question 18

When is the slope-intercept form used?

Answer 18

When the slope and the coordinates of the y-intercept of a linear graph are available.

Question 19

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

Answer 19

f(x) = mx + b.

Question 20

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

Answer 20

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 21

What does b mean in the slope-intercept form?

Answer 21

The y-coordinate of the y-intercept.

Question 22

What does m mean in the slope-intercept form?

Answer 22

m is the slope.

Question 23

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

Answer 23

Slope-intercept.

Question 24

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

Answer 24

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

Question 25

Can horizontal linear graphs be graphs of functions?

Answer 25

Yes, they always are.

Question 26

Can vertical linear graphs be graphs of functions?

Answer 26

No.

Question 27

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

Answer 27

Yes.

Question 28

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

Answer 28

Standard\general.

Question 29

What is a scatter plot, aka. scatter graph?

Answer 29

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

Question 30

What is a regression line?

Answer 30

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.