Writing Linear Equations in Standard Form

Front

What is the slope-intercept form of a line?

Back

The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

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 from 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 does the slope (m) represent in a linear equation?

Back

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

Front

What is the y-intercept (b) in the slope-intercept form?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented as (0, b).

Front

Write the standard form of the equation for the line: y = 1/4 x + 4

Back

The standard form is x - 4y = -16.

Front

What is point-slope form of a linear equation?

Back

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you identify if an equation is in standard form?

Back

An equation is in standard form if it can be expressed as Ax + By = C, where A, B, and C are integers.

Front

What is the relationship between slope and parallel lines?

Back

Parallel lines have the same slope (m) but different y-intercepts (b).

Front

What is the relationship between slope and perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other, meaning if one line has a slope of m, the other has a slope of -1/m.