24-25 Alg1 3-5 FLASHCARD - Point-slope & direct variation

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed in the form y = kx, where k is a non-zero constant.

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 can you identify a direct variation graph?

Back

A graph represents direct variation if it passes through the origin (0,0) and is a straight line.

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the relationship between direct variation and proportionality?

Back

Direct variation indicates a proportional relationship between two variables, meaning that as one variable increases, the other variable increases at a constant rate.

Front

How do you convert a point-slope equation 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 significance of the constant k in the equation y = kx?

Back

The constant k in the equation y = kx represents the constant of variation, indicating how much y changes for a unit change in x.

Front

What is an example of a direct variation equation?

Back

An example of a direct variation equation is y = 3x, where y varies directly with x with a constant of variation k = 3.

Front

How can you determine if a set of points represents a direct variation?

Back

To determine if a set of points represents direct variation, check if the ratio of y to x is constant for all points.

Front

What is the formula for finding the slope between two points (x1, y1) and (x2, y2)?

Back

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