Slope and Equations of Lines

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation. It is calculated as the change in y divided by the change in x (rise over run).

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 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

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means that one line has a slope that is the negative reciprocal of the other.

Front

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

Back

The point-slope form of a linear equation is given by 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 from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y to isolate it on one side.

Front

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

Back

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

Front

What is an undefined slope?

Back

An undefined slope occurs in vertical lines, where the change in x is zero, leading to division by zero in the slope formula.

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope and different y-intercepts.