Equations of Lines

Front

What is the slope-intercept form of a line?

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

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

How do you find the y-intercept of a line from its equation?

Back

The y-intercept can be found by setting x = 0 in the equation and solving for y.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = a, where a is the x-coordinate of any point on the line.

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = b, where b is the y-coordinate of any point on the line.

Front

How do you convert the standard form of a line to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y to get y = (-A/B)x + (C/B).

Front

What is the significance of the 'b' value in the equation y = mx + b?

Back

The 'b' value represents the y-intercept, which is the point where the line crosses the y-axis.

Front

If a line has a slope of 0, what type of line is it?

Back

A line with a slope of 0 is a horizontal line.

Front

If a line has an undefined slope, what type of line is it?

Back

A line with an undefined slope is a vertical line.

Front

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

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).