Post Test Quiz on Linear Relationships

Questions and Answers

Which graph represents this equation -3x + 4y = -12?

(0, -3) and (4, 0) (correct)

(-3, -3) and (-3, 3)

(0, 2) and (1, -3)

(-4, 1) and (-3, -2)

The slope of the graphed line is positive.

True

Which graph represents this equation y − 4 = -3(x + 5)?

(0, 2) and (1, -3)

(-4, 1) and (-3, -2) (correct)

(-3, -3) and (-3, 3)

(0, -3) and (4, 0)

What is the slope of the line that goes through the points (1, -5) and (4, 1)?

2 Signup and view all the answers

Which number best represents the slope of the graphed line?

-5 Signup and view all the answers

Graph the line that represents this equation: y = -5x + 2, the points are: (0, 2) and (1, ___)

-3 Signup and view all the answers

Which two points have an undefined slope?

(-3, -3) and (-3, 3) Signup and view all the answers

Determine which graph and which equation represent the amount of money Chelsea earns in one day, A, after taking w walks with the dogs.

A = 2.5w + 12, points: (8, 32) and (0, 12) Signup and view all the answers

What is the equation of the line that has a slope of 3 and goes through the point (-3, -5)?

y = 3x + 4 Signup and view all the answers

What is the slope of the line shown in the graph of the concert ticket sales?

-400 Signup and view all the answers

Which graph represents the balance of the cash box, y, after Jackie sells x smoothies?

points: (0, 15) and (4, 30) Signup and view all the answers

Which equation represents the height of fudge brownies with x teaspoons of baking powder?

y = 0.28x + 0.75 Signup and view all the answers

Which equation describes the line graphed above?

y = -1/5x - 4 Signup and view all the answers

What is the range of the relationship between Charlotte and Travis's employment years?

y is three years greater than x Signup and view all the answers

If the graph of f(x) = x is shifted up 9 units, what would be the equation of the new graph?

g(x) = f(x) + 9 Signup and view all the answers

What is the y-intercept of g for the functions f(x) = -3x - 5 and g(x) = f(x) + 9?

4 Signup and view all the answers

Graph the line representing function g, if g is defined as g(x) = f(x) + 4.

points: (0, 1) and (-2, 0) Signup and view all the answers

Which statement correctly describes the graph of function g if g(x) = -8f(x)?

It is a vertical stretch of f(x). Signup and view all the answers

Consider the function g, which has a y-intercept of -2. Which of the following functions could represent g?

g(x) = f(x) - 5 Signup and view all the answers

Which statement correctly describes the graph of g(x) if g(x) = f(x) - 3?

It is the graph of f(x) translated 3 units down. Signup and view all the answers

Study Notes

Linear Relationships and Graphs

The equation -3x + 4y = -12 is represented by graph points (0, -3) and (4, 0).
Positive slope indicates that as x increases, y also increases.

Slope Calculations

The slope of a line through points (1, -5) and (4, 1) is calculated as 2.
A slope of -5 signifies a decreasing function.

Graphing Lines

For the equation y = -5x + 2, key points are (0, 2) and (1, -3).
An undefined slope occurs with vertical lines, exemplified by points (-3, -3) and (-3, 3).

Real-world Applications

Chelsea earns money based on a formula A = 2.5w + 12, indicated by graph points (8, 32) and (0, 12).
Jackie’s cash box balance after selling x smoothies can be represented with points (0, 15) and (4, 30).

Equation Representation

The fudge brownie height relationship is expressed by y = 0.28x + 0.75 based on baking powder measurements.
The equation y = -1/5x - 4 represents a specific graph line.

Relationship Analysis

Travis has worked 3 years more than Charlotte, establishing a direct relationship between their work durations.
The new equation after shifting f(x) = x up 9 units becomes g(x) = f(x) + 9.

Function Transformation

The y-intercept of g, derived from f(x) = -3x - 5 adjusted by +9, requires calculation.
g(x) = f(x) + 4 reflects a vertical shift upward of function f.

Vertical Shifts and Translations

A transformation represented by g(x) = -8f(x) indicates reflection and vertical stretch.
A y-intercept of -2 for function g suggests a downward shift, expressed as g(x) = f(x) - 5.
The transformation g(x) = f(x) - 3 indicates a downward translation of 3 units from f(x).

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Description

Test your understanding of linear relationships with this quiz based on Algebra 1A Unit 4. It includes questions on graphing linear equations and analyzing slopes. Perfect for reinforcement and review of key algebra concepts.

Algebra 1A- Unit 4- Post Test on Linear Relationships