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

Identify the general form of a linear equation in point-slope form.

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

How can you determine if a graph represents a direct variation?

Back

A graph represents direct variation if it passes through the origin (0,0) and is a straight line.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3.

Front

If a line has a slope of -2, what does this indicate about the line's direction?

Back

A slope of -2 indicates that the line descends from left to right, meaning as x increases, y decreases.

Front

What is the y-intercept in the equation y = 4x - 5?

Back

The y-intercept is -5, which is the point where the line crosses the y-axis.

Front

Convert the point-slope equation y - 2 = 3(x - 1) to slope-intercept form.

Back

The slope-intercept form is y = 3x - 1.

Front

What is the relationship between direct variation and proportionality?

Back

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

Front

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

Back

The constant of variation k is 4, since k = y/x = 12/3.