Equations of Lines and Slope

Front

What is the definition of slope in the context of a graph?

Back

Slope is a measure of the steepness or incline of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

True or False: The slope of a line can be represented by a right triangle on a graph.

Back

True.

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 calculate 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 does a positive slope indicate about a line on a graph?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a line on a graph?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, resulting in a downward slant of the line.

Front

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

Back

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

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) but different y-intercepts (b).

Front

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

Back

Two lines are perpendicular if the product of their slopes is -1 (i.e., m1 * m2 = -1).

Front

What is the formula for 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.