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 the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

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 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.