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Questions and Answers
Which of the following equations represents the inverse of the function $f(x) = 6x - 3$?
Which of the following equations represents the inverse of the function $f(x) = 6x - 3$?
- $f^{-1}(x) = rac{1}{6}x + rac{1}{2}$ (correct)
- $f^{-1}(x) = rac{1}{6}x - rac{1}{3}$
- $f^{-1}(x) = -6x + 3$
- $f^{-1}(x) = - rac{1}{6}x - rac{1}{2}$
Which line is perpendicular to $y = - rac{3}{4}x + 2$?
Which line is perpendicular to $y = - rac{3}{4}x + 2$?
- $y = rac{3}{4}x - 2$
- $y = - rac{3}{4}x - 5$
- $y = - rac{4}{3}x + 3$
- $y = rac{4}{3}x + 1$ (correct)
Which line is parallel to $y = -7x + 5$?
Which line is parallel to $y = -7x + 5$?
- $y = 7x - 5$
- $y = -\frac{1}{7}x - 2$
- $y = -7x - 2$ (correct)
- $y = \frac{1}{7}x + 5$
A line parallel to $y = 5x - 3$ passes through the point $(2, 7)$. What is its equation in slope-intercept form?
A line parallel to $y = 5x - 3$ passes through the point $(2, 7)$. What is its equation in slope-intercept form?
A line perpendicular to $y = -2x + 1$ passes through the point $(-4, 3)$. Give its equation in slope-intercept form.
A line perpendicular to $y = -2x + 1$ passes through the point $(-4, 3)$. Give its equation in slope-intercept form.
A line has a slope of -2 and passes through the point (4, -5). Express this line in point-slope form.
A line has a slope of -2 and passes through the point (4, -5). Express this line in point-slope form.
Given the points (1, -1) and (3, 3), determine the slope (m) and y-intercept (b) of the line that passes through them.
Given the points (1, -1) and (3, 3), determine the slope (m) and y-intercept (b) of the line that passes through them.
A taxi charges an initial fee of $4.00 plus $2.50 per mile. Write an equation in slope-intercept form to model the total cost, y, for x miles.
A taxi charges an initial fee of $4.00 plus $2.50 per mile. Write an equation in slope-intercept form to model the total cost, y, for x miles.
Flashcards
Inverse of a Function
Inverse of a Function
A function's inverse undoes the original function's operation.
Perpendicular Line
Perpendicular Line
A line perpendicular to another has a slope that is the negative reciprocal.
Parallel Line
Parallel Line
A line parallel to another has the same slope.
Point-Slope Form
Point-Slope Form
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Slope and Y-Intercept
Slope and Y-Intercept
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Slope-Intercept Model
Slope-Intercept Model
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Point-Slope Formula
Point-Slope Formula
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Point-Slope Components
Point-Slope Components
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Study Notes
- These notes cover linear equations, point-slope form, slope-intercept form, parallel and perpendicular lines, and inverse functions
Finding the Inverse of a Function
- To find the inverse of the function f(x) = -4x + 2, it is f⁻¹(x) = -x/4 + ½.
Perpendicular and Parallel Lines Equations
Perpendicular
- Determine which line is perpendicular to y = (1/5)x
- The perpendicular line is y = -5x + 1.
Parallel
- Find the line parallel to y = (2/5)x + 2.
- The parallel line is y = (2/5)x + 2 as parallel lines will always have the same slope
Equation Forms
Parallel Equation
- For a line parallel to y = (1/3)x + 2 passing through (3, -2)
- The equation is y = (1/3)x - 3.
- Parallel lines have the same slope.
Perpendicular Equation
- Determine a line perpendicular to y = (1/3)x + 2 through (3, -2):
- It is y = -3x + 7
- Line slope becomes the negative reciprocal.
Point-Slope Form
- For a line through (8, 33) with a slope of 3:
- Formula y -y₁ = m(x - x₁)
- The equation is (y - 33) = 3(x - 8)
Slope-Intercept Form
- General Formula: y = mx + b, where m is the slope and b is the y-intercept.
- Given points (2, 4) and (-4, 1), the equation of the line is:
- y = (1/2)x + 3
- For a movie theater popcorn cost, where refills are $2.50 and the initial bucket is $3.50:
- The total cost equation is y = 2.5x + 3.5
- For point (5, -2) with a slope of 4.
- The equation is y = 4x - 22
- Slope-intercept form given (y - 12) = -2(x + 4):
- The equation of the line, is y = -2x - 20
Point-Slope Equation Details
- For the equation y + 3 = 4(x + 7):
- m = 4, x₁ = -7, and y₁ = -3
- Given points (3, 2) and (1, -2) write an equation:
- The equation is (y - 2) = 2(x - 3)
Inverse Functions
- Select ordered pairs that are the inverse of the function: {(1, 1), (–½, 2), (7, 3)}
- Select the three ordered pairs showing the inverse of the relation on the graph: (-3, -2), (-2, 0), and (-1, 2)
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Description
Explore linear equations: finding inverse functions, identifying parallel and perpendicular lines, and using point-slope form. Examples show how to determine equations of parallel lines, perpendicular lines, and inverses of functions.
