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 y with respect to x. It indicates how much y changes for a unit change in x.

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 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 in the equation y = -2x + 5?

Back

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

Front

If a line has a slope of -1, what does this indicate about the line's direction?

Back

A slope of -1 indicates that the line descends from left to right.