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 can 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

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

Back

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

Front

What is the equation of a line in slope-intercept form?

Back

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert from point-slope form to slope-intercept form?

Back

To convert, solve for y in the point-slope equation y - y1 = m(x - x1) to get y = mx + (y1 - mx1).

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

If a line has a slope of 2 and passes through the point (1, 3), what is its equation in point-slope form?

Back

The equation is y - 3 = 2(x - 1).

Front

What does it mean if two variables are inversely related?

Back

If two variables are inversely related, as one variable increases, the other decreases, typically expressed as y = k/x.