Equations of Lines and Slope

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 ratio of the rise (change in y) over the run (change in x).

Front

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

Back

The slope-intercept form of a linear equation is given by the equation 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 does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line falls from left to right.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

What is the relationship between the slope of a line and the angle it makes with the x-axis?

Back

The slope of a line is equal to the tangent of the angle (θ) it makes with the positive x-axis, where m = tan(θ).

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope (m).

Front

How can you determine if two lines are perpendicular using their slopes?

Back

Two lines are perpendicular if the product of their slopes (m1 * m2) equals -1.

Front

What is the formula for the equation of a line given a point and the slope?

Back

The equation of a line can be written using point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.