Equations of Lines

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 the standard form of a linear equation to slope-intercept form?

Back

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

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

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

Back

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

Front

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

Back

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

Front

What is the equation of a vertical line?

Back

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

Front

How do you write the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), substituting the slope (m) and the coordinates of the point (x1, y1).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the coordinate (0, b) in the slope-intercept form.

Front

What does it mean if a line has an undefined slope?

Back

An undefined slope indicates a vertical line, where the change in x is zero, leading to division by zero.