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 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 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 from point-slope form 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 direct variation equation y = kx?

Back

The constant k represents the constant of variation, indicating how much y changes for each unit change in x. It is the slope of the line in the graph.

Front

Can a linear equation have both point-slope and slope-intercept forms?

Back

Yes, a linear equation can be expressed in both point-slope form and slope-intercept form, as they are different representations of the same line.

Front

What is an example of a direct variation equation?

Back

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

Front

How do 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.