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

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 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

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 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 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 y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

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

Back

A set of points represents direct variation if the ratio of y to x is constant for all points.

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx, where k is the constant of variation.

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 direct variation, as direct variation requires that the relationship starts at the origin.