Writing 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 (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

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

Front

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

Back

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

Front

What is the y-intercept of a line?

Back

The y-intercept of a line is the point where the line crosses the y-axis, represented as 'b' in the slope-intercept form (y = mx + b).

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 to isolate it on one side of the equation.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is expressed as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.

Front

How do you determine the slope from a linear equation in standard form?

Back

To find the slope from a linear equation in standard form (Ax + By = C), rearrange the equation to slope-intercept form (y = mx + b) and identify 'm'.

Front

What is the significance of the 'b' value in the slope-intercept form?

Back

The 'b' value in the slope-intercept form (y = mx + b) represents the y-coordinate of the point where the line crosses the y-axis.