Linear Equations and Their Applications

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is expressed as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, found by setting x = 0 in the equation.

Front

How can you write a linear equation in slope-intercept form?

Back

The slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the meaning of the slope in a real-world context?

Back

In a real-world context, the slope can represent a rate, such as speed or cost per item.

Front

How do you convert a linear equation from slope-intercept form to standard form?

Back

To convert, rearrange the equation to the form Ax + By = C, ensuring A, B, and C are integers.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients indicate the relationship between the variables; for example, the coefficient of x represents the change in y for a unit change in x.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find the x-intercept and y-intercept, plot these points, and draw a line through them.

Front

What is a linear relationship?

Back

A linear relationship is one where there is a constant rate of change between two variables, represented by a straight line on a graph.