Converting Linear Equations between forms

Front

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

Back

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

Front

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

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What is 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

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 by the value of y when x = 0.

Front

Convert the equation 3x - 5y = 15 to slope-intercept form.

Back

y = (3/5)x - 3.

Front

What is the relationship between the coefficients in standard form and the slope?

Back

In standard form Ax + By = C, the slope is given by -A/B.

Front

How do you determine 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

Convert the equation y = 2x + 3 to standard form.

Back

2x - y = -3.