Algebra 2 - 2.2, 2.4, 2.7 Problems Flashcards

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Questions and Answers

Write an equation in point-slope form for the points (1/2, 2/3) and (-3/2, 5/3).

y - 2/3 = -1/2(x - 1/2)

Write an equation in standard form for the slope 2/5 and the point (-1, 3).

y - 2/5x = 3.4

Find the slope and intercepts of the line f(x) = 4/5x + 7.

x intercept = -35/4, 0 ; y intercept = 0, 7

Write an equation for the line that goes through (-1, 3) and is parallel to y = 2x + 1.

y = 2x + 5 Signup and view all the answers

Write an equation for the line that goes through (-3, 4) and is vertical.

x = -3 Signup and view all the answers

What is the cost to produce 12 units if the cost of producing 4 units is $204.80 and the cost of producing 8 units is $209.60?

$214.4 Signup and view all the answers

How many subscribers will there be after 10 months if there were 5730 subscribers after 5 months and 6022 after 7 months?

6460 Signup and view all the answers

Is the set {(1,-2), (2, 3/4), (3, 3 + 1/2), (5, 9)} a function or relation?

Function Signup and view all the answers

Is the set {(0.5, -1), (0.5, 0), (0.5, 1), (0.5, 3)} a function or relation?

Relation Signup and view all the answers

Is the set {(-3, 5), (0, -2), (0, 4), (1, -2)} a function or relation?

Relation Signup and view all the answers

For the function f(x) = 5x + 2, find f(-2), f(3), f(7).

(-2, -8), (3, 17), (7, 37) Signup and view all the answers

For the function f(x) = -1/3x + 1, find f(-2), f(3), f(7).

(-2, 5/3), (3, 0), (7, -4/3) Signup and view all the answers

For the function f(x) = -3x + 1.8, find f(-2), f(3), f(7), f(-1/2).

((-2, 7.8), (3, -7.2), (7, -19.2), (-1/2, 3.3)) Signup and view all the answers

What is g(-2)/f(3) if f(x) = -3x + 2 and g(x) = 1/2x - 1?

2/7 Signup and view all the answers

What does a DOTTED line mean when graphing two-variable inequalities?

Less than or greater than. Signup and view all the answers

What does a SOLID line mean when graphing two-variable inequalities?

Less than or equal to, or greater than or equal to. Signup and view all the answers

Find the slope of the line through the points (2, 3) and (-5, -9).

12/7 Signup and view all the answers

Solve for y, slope (m), and y-intercept (b) in the equation 8x - 2y = 9.

y = 4x - 3 ; m = 4 ; b = -3 Signup and view all the answers

Study Notes

Point-Slope and Standard Form Equations

Point-slope form equation derived from points (1/2, 2/3) and (-3/2, 5/3) is y - 2/3 = -1/2(x - 1/2)
Standard form for a line with slope 2/5 through the point (-1, 3) simplifies to y - 2/5x = 3.4.

Slope and Intercepts

For the linear function f(x) = 4/5x + 7:
- x-intercept is (-35/4, 0)
- y-intercept is (0, 7).

Parallel and Vertical Lines

An equation for a line parallel to y = 2x + 1 through (-1, 3) is y = 2x + 5.
A vertical line through (-3, 4) is represented as x = -3 (undefined slope).

Cost Calculations

Cost of producing 12 units after producing 4 units for $204.80 and 8 units for $209.60 is $214.4.

Subscriber Growth

Subscribers increased from 5730 after 5 months to 6022 after 7 months. The projection for 10 months is 6460 subscribers.

Functions vs. Relations

Set { (1, -2), (2, 3/4), (3, 3+1/2), (5, 9) } is categorized as a Function.
Set { (0.5, -1), (0.5, 0), (0.5, 1), (0.5, 3) } is categorized as a Relation due to repeating x-values.
Set { (-3, 5), (0, -2), (0, 4), (1, -2) } is categorized as a Relation for the same reason.

Function Evaluations

For the function f(x) = 5x + 2:
- f(-2) = -8, f(3) = 17, f(7) = 37 gives pairs (-2, -8), (3, 17), (7, 37).
For f(x) = -1/3x + 1:
- Evaluations yield f(-2) = 5/3, f(3) = 0, f(7) = -4/3 resulting in (-2, 5/3), (3, 0), (7, -4/3).
For f(x) = -3x + 1.8:
- Calculated values provide (-2, 7.8), (3, -7.2), (7, -19.2), (-1/2, 3.3).

Composite Functions

For functions f(x) = -3x + 2 and g(x) = 1/2x - 1, calculating g(-2) / f(3) yields 2/7.

Graphing Inequalities

A DOTTED line in graphing two-variable inequalities indicates relationships of less than or greater than.
A SOLID line indicates relationships of less than or equal to, or greater than or equal to.

Slope Calculation

Calculating slope between points (2, 3) and (-5, -9) yields a slope of 12/7.

Rearranging Linear Equations

Rearranging the equation 8x - 2y = 9 results in the slope-intercept form y = 4x - 3, with slope m = 4 and y-intercept b = -3.

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Description

Test your understanding of key concepts from Algebra 2 through challenging problems on point-slope and standard form equations. This quiz covers various aspects including finding slopes and intercepts of lines. Perfect for revision or self-assessment!