Converting Linear Equations between forms

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

Convert the equation y = 3x - 5 to standard form.

Back

3x - y = 5.

Front

What is slope-intercept form?

Back

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

Front

Convert the equation 2x + 3y = 6 to slope-intercept form.

Back

y = -2/3x + 2.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

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 slope-intercept form.

Front

Convert the equation x - 2y = -6 to slope-intercept form.

Back

y = 1/2x + 3.

Front

What is the relationship between standard form and slope-intercept form?

Back

Standard form can be converted to slope-intercept form by solving for y.

Front

Match the equation 3x - 5y = 1 to its graph.

Back

The graph of this equation will have a slope of 3/5 and a y-intercept of 1/5.