Standard Form Linear Equations

Front

What is the standard form of a linear equation?

Back

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

Front

How do you convert the slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to isolate the variables on one side.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the slope-intercept form y = mx + b.

Front

How do you find the slope from a standard form equation?

Back

To find the slope from a standard form equation Ax + By = C, rearrange it to slope-intercept form (y = mx + b) and identify the coefficient m.

Front

What does the slope of a line represent?

Back

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

Front

What is the relationship between the slope and the angle of a line?

Back

The slope of a line is the tangent of the angle (θ) that the line makes with the positive x-axis.

Front

How can you determine if two lines are parallel using their equations?

Back

Two lines are parallel if they have the same slope. In standard form, if the ratios of the coefficients of x and y are equal, the lines are parallel.

Front

What is the significance of the coefficients A and B in the standard form of a linear equation?

Back

In the standard form Ax + By = C, A and B determine the slope and direction of the line. A represents the change in y for a unit change in x.

Front

How do you graph a linear equation in standard form?

Back

To graph a linear equation in standard form, find the x-intercept (set y=0) and y-intercept (set x=0), then plot these points and draw a line through them.

Front

What is the x-intercept of a linear equation?

Back

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