Review and Practice (Domains, Range, Writing Linear Equations)

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line, and is calculated as the ratio of the change in the y-coordinate to the change in the x-coordinate between two points on the line.

Front

What does a zero slope indicate about a line?

Back

A zero slope indicates that the line is horizontal, meaning there is no change in the y-coordinate as the x-coordinate changes.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning the x-coordinate does not change while the y-coordinate changes.

Front

How do you determine the domain of a function from its graph?

Back

The domain of a function is determined by identifying all the possible x-values (inputs) for which the function is defined, typically read from left to right on the graph.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce, based on its domain.

Front

How do you write the equation of a line given its slope and a point?

Back

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

Front

What is the formula to 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

If a line passes through the points (3, 5) and (-2, 2), what is the slope?

Back

The slope is calculated as m = (2 - 5) / (-2 - 3) = -3 / -5 = 3/5.

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 does it mean if a line has a positive slope?

Back

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