Standard Form of 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 a 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 get all terms involving x and y on one side and the constant on the other.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

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

Back

The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the y-intercept of a line?

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

Write the standard form of the equation of the line through (1, 2) and (3, 4).

Back

The standard form is 1x - 1y = -1.

Front

What is the relationship between slope and parallel lines?

Back

Parallel lines have identical slopes, meaning they rise and run at the same rate.

Front

Write the slope-intercept form of the equation of the line with slope 2 and y-intercept -3.

Back

The slope-intercept form is y = 2x - 3.

Front

How do you determine the x-intercept of a line?

Back

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