Linear Equation Forms

Front

What is the point-slope form of a linear equation?

Back

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

Front

How do you find the y-intercept from a linear equation in standard form?

Back

To find the y-intercept from the standard form Ax + By = C, set x = 0 and solve for y.

Front

What is the standard form of a linear equation?

Back

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

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

How do you convert from point-slope form to slope-intercept form?

Back

To convert, solve for y in the point-slope form equation y - y₁ = m(x - x₁) to get y = mx + (y₁ - mx₁).

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 x-intercept of a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis, found by setting y = 0 and solving for x.

Front

What is the significance of the coefficients in standard form?

Back

In standard form Ax + By = C, A represents the coefficient of x, B represents the coefficient of y, and C is the constant term.

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed, typically in the form y = mx + b.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope but different y-intercepts.