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 direct variation graph is a straight line that passes through the origin (0,0).

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

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 y varies directly with x and y = 12 when x = 4, what is the constant of variation (k)?

Back

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

Front

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

Back

The slope-intercept form of a line is given by 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 from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the y-intercept of the line represented by the equation y = -2x + 5?

Back

The y-intercept is 5, which is the value of y when x = 0.

Front

What does it mean if two variables are in direct variation?

Back

If two variables are in direct variation, it means that as one variable increases, the other variable also increases proportionally.