Linear Functions and Slopes Flashcards
What does the word slope mean?
The measure of steepness.
What does the rise of a slope indicate?
The vertical change.
What does the run of a slope indicate?
The horizontal change.
What is the point-slope form of an equation of a line?
y - y₁ = m(x - x₁).
What’s the difference between (x, y) and (x₁, y₁)?
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.
What’s a positive slope?
An increasing slope.
What’s a negative slope?
A decreasing slope.
What’s a constant slope?
A line who’s slope is 0.
Does a horizontal line have a slope?
Yes.
What’s the slope of a vertical line.
Undefined.
What is the slope if m > 0?
Positive, aka increasing.
What is the slope if m < 0?
Negative, aka decreasing.
What is the slope if m = 0?
Constant, aka zero slope, aka horizontal line.
What is the slope if m is undefined?
Undefined slope.
What information is needed for finding the equation of a linear graph using the point-slope form?
The slope and a point on the line graph.
When is the point-slope form used?
When the slope and an arbitrary point on the line graph are available.
What is the slope-intercept form of the equation of a line?
y = mx + b, where m is the slope and b is the y intercept.
When is the slope-intercept form used?
When the slope and the coordinates of the y-intercept of a linear graph are available.
How does the slope-intercept form look like in function notation?
f(x) = mx + b.
How do we obtain a graph using the slope-intercept form?
- plot the y-intercept point
- using the slope, count the vertical change and the corresponding horizontal change and plot a point, starting at the y-intercept point
- using a straightedge draw a line between the two points
What does b mean in the slope-intercept form?
The y-coordinate of the y-intercept.
What does m mean in the slope-intercept form?
m is the slope.
What’s the name of this form of the line of an equation: f(x) = mx + b?
Slope-intercept.
What causes the slope-intercept form to turn into y = b?
If m is 0 the term mx is nulified and what’s left is y = b.
Can horizontal linear graphs be graphs of functions?
Yes, they always are.
Can vertical linear graphs be graphs of functions?
No.
Is this the equation of a line: 3x + 6y = 2?
Yes.
In what form is this linear equation: x + 2y = -6
Standard\general.
What is a scatter plot, aka. scatter graph?
Data presented in a visual form as a set of points.
What is a regression line?
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.
