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

Front

What is the definition of direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, typically 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 the formula 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 direct variation graph is a straight line that passes through the origin (0,0).

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 much y changes for a unit change in x.

Front

What is the relationship between the slope and direct variation?

Back

In direct variation, the slope (k) is the constant of variation, meaning that the ratio of y to x is constant.

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 an example of a direct variation equation?

Back

An example of a direct variation equation is y = 3x, where 3 is the constant of variation.

Front

What is the significance of the constant of variation in direct variation?

Back

The constant of variation (k) indicates how much y changes for each unit change in x; it is the slope of the line in a direct variation.

Front

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

Back

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

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.