Algebra 1 Chapter 4 Test Review

Questions and Answers

Is the ordered pair (2, -4/5) a solution of the equation $5x + 3y = 2$?

False

What is the x-intercept of the equation $4x + 5y = 8$?

x = 2

What is the y-intercept of the equation $7 - 12x = 3y$?

y = 7/3

What is the slope of the line passing through the points (-10, -7) and (1, -2)?

m = -5/11 Signup and view all the answers

What is the value of y for the line passing through the points (6, y) and (3, 3) with slope $m = 2/3$?

y = 5 Signup and view all the answers

What is the average rate of change (slope) of the software company's profit from 1999 to 2005?

$30m per year Signup and view all the answers

What is the equation relating x and y if they vary directly and x = -6, y = 42?

y = -7x Signup and view all the answers

Which of the following are conditions for direct variation? (Select all that apply)

The y-intercept is equal to 0 Signup and view all the answers

Are the graphs of the functions $f(x) = 3x + 2$ and $f(x) = rac{1}{3}x + 4$ parallel?

False Signup and view all the answers

What is the value of the function $f(x) = -7x - 3$ at $x = -17$?

(-17, 116) Signup and view all the answers

Study Notes

Ordered Pairs and Solutions

An ordered pair (2, -4/5) does not satisfy the equation 5x + 3y = 2, leading to 7 3/5 ≠ 2.

Intercepts

The x-intercept of the equation 4x + 5y = 8 is found at x = 2.
The y-intercept of the equation 7 - 12x = 3y is y = 7/3.

Slope Calculation

The slope (m) of the line through points (-10, -7) and (1, -2) is calculated as m = -5/11.
To achieve a slope of 2/3 through the points (6, y) and (3, 3), the value of y must be 5.

Average Rate of Change

From 1999 ($30 million profit) to 2005 ($210 million profit), the average rate of change in profit is $30 million per year, representing the linear growth over 6 years.

Direct Variation

Direct variation between variables x and y can be described by the equation y = -7x, using the values x = -6 and y = 42 for derivation.

Conditions for Direct Variation

For a relationship to be classified as direct variation, two conditions must be met:
- The y-intercept must be equal to 0.
- The graph of the function displays a straight line passing through the origin.

Parallel Lines Assessment

The functions f(x) = 3x + 2 and f(x) = 1/3x + 4 do not represent parallel lines as their slopes differ.

Function Evaluation

Evaluating the function f(x) = -7x - 3 at x = -17 results in an ordered pair (-17, 116).

Description

Prepare for your Algebra 1 Chapter 4 test with these review flashcards. Each card presents a key concept such as ordered pairs, intercepts, and slope calculations. Test your skills and improve your understanding of linear equations and graphing!