Equation of a line

Front

What is the general form of the equation of a line?

Back

The general form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine the slope of a line from two points?

Back

The slope (m) of a line through two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the y-intercept represent in the equation of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A line with a slope of 0 is horizontal, indicating that the y-value remains constant regardless of the x-value.

Front

What is the slope of a line that is vertical?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero in the slope formula.

Front

How can you find the equation of a line given a point and the slope?

Back

You can use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the slope-intercept form of a line?

Back

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

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: y = (-A/B)x + (C/B).

Front

What is the significance of a negative slope?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line from left to right.

Front

What is the equation of a line with a slope of 2 and a y-intercept of -3?

Back

The equation of the line is y = 2x - 3.