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 difference between direct variation and inverse variation?

Back

In direct variation, as one variable increases, the other also increases. In inverse variation, as one variable increases, the other decreases.

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 direct variation?

Back

The constant 'k' in direct variation represents the constant of proportionality, indicating how much y changes for a unit change in x.

Front

How can you determine the slope from a graph?

Back

The slope can be determined by selecting two points on the line, calculating the rise (change in y) over the run (change in x) between those points.

Front

What is an example of a real-world situation that can be modeled by direct variation?

Back

An example of direct variation is the relationship between distance and time when traveling at a constant speed.

Front

What is the formula for direct variation?

Back

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