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 as 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 do 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 y with respect to x, indicating how much y changes for a unit change in x.

Front

What is the constant of variation in direct variation?

Back

The constant of variation (k) is the non-zero constant in the equation y = kx, representing the ratio of y to x.

Front

If y varies directly with x and y = 12 when x = 3, what is the constant of variation?

Back

k = y/x = 12/3 = 4.

Front

What is the relationship between direct variation and proportionality?

Back

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

Front

How can 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.

Front

What is an example of a direct variation equation?

Back

An example of a direct variation equation is y = 5x.

Front

What does it mean if a graph does not pass through the origin?

Back

If a graph does not pass through the origin, it does not represent a direct variation.