Study Guide ACP Review

Front

What is the solution to the equation −5x−4(2x−6)+3=6(5−2x)+11x?

Back

The solution is x = -\frac{1}{4}.

Front

If the total cost of gas, y, varies directly with the amount of gas purchased, x, and 5 1/2 gallons cost $12.60, what is the equation that represents this relationship?

Back

The equation is y = 2.40x.

Front

In a weight loss graph, what does the y-intercept represent?

Back

The y-intercept represents the initial weight before any weight loss.

Front

If Raymond spray-painted 25 desks from 8:00 a.m. to 1:00 p.m., how long will it take him to spray-paint 570 desks?

Back

It will take him 114 hours.

Front

What is the general form of a direct variation equation?

Back

The general form is y = kx, where k is the constant of variation.

Front

How do you find the slope of a line given two points?

Back

The slope m is calculated as m = \frac{y_2 - y_1}{x_2 - x_1}.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x = 0.

Front

How can you determine if a function is linear?

Back

A function is linear if it can be written in the form y = mx + b, where m and b are constants.

Front

What does the term 'direct variation' mean?

Back

Direct variation means that two quantities increase or decrease together at a constant rate.