Modified Point-Slope Form + Inverse Practice
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the modified point-slope form of a linear equation?
Back
The modified point-slope form is given by the equation: y = m(x - x_0) + y_0, where m is the slope and (x_0, y_0) is a point on the line.
2.
FLASHCARD QUESTION
Front
How do you find the equation of a line given a slope and a point?
Back
Use the modified point-slope form: y = m(x - x_0) + y_0, substituting the slope (m) and the coordinates of the point (x_0, y_0).
3.
FLASHCARD QUESTION
Front
What is the slope of a line?
Back
The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change to the horizontal change between two points on the line.
4.
FLASHCARD QUESTION
Front
How do you convert from point-slope form to slope-intercept form?
Back
To convert, expand the point-slope form equation y = m(x - x_0) + y_0 to the form y = mx + b, where b is the y-intercept.
5.
FLASHCARD QUESTION
Front
What is the inverse of a function?
Back
The inverse of a function f(x) is a function f^{-1}(x) that reverses the effect of f, such that f(f^{-1}(x)) = x for all x in the domain.
6.
FLASHCARD QUESTION
Front
How do you find the inverse of a linear function?
Back
To find the inverse of a linear function f(x) = mx + b, swap x and y, then solve for y: y = (x - b)/m.
7.
FLASHCARD QUESTION
Front
What is the significance of the slope in a linear equation?
Back
The slope indicates the direction and steepness of the line; a positive slope means the line rises, while a negative slope means it falls.
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