Writing Linear Equations in Various 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 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 + b.

Front

What is the standard form of a linear equation?

Back

The standard form is given by 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 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 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 write an equation in standard form from two points?

Back

First, find the slope using the two points, then use the point-slope form to write the equation, and finally rearrange it to standard form.

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 by the value of b in the slope-intercept form y = mx + b.

Front

How do you rewrite an equation from slope-intercept form to standard form?

Back

To convert, rearrange the equation y = mx + b to the form Ax + By = C by moving all terms to one side.

Front

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

Back

A and B indicate the direction and steepness of the line; if A is positive, the line slopes upwards as you move from left to right.