Algebra 1 SOL Review #4

Front

What is inverse variation?

Back

Inverse variation occurs when one variable increases while the other decreases, such that their product is constant. For example, if the temperature decreases, the number of layers of clothes needed increases.

Front

What is direct variation?

Back

Direct variation occurs when two variables increase or decrease together, maintaining a constant ratio. For example, if x varies directly with y, then as x increases, y also increases.

Front

How do you find the missing value in direct variation?

Back

To find the missing value in direct variation, use the formula \( y = kx \), where k is the constant of variation. Rearrange the equation to solve for the missing variable.

Front

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

Back

The equation of a line in slope-intercept form is given by \( y = mx + b \), where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form \( ax^2 + bx + c = 0 \), where a, b, and c are constants and a ≠ 0.

Front

How do you solve a quadratic equation?

Back

Quadratic equations can be solved using factoring, completing the square, or the quadratic formula: \( x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: \( b^2 - 4ac \). It determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

What is a line of best fit?

Back

A line of best fit is a straight line that best represents the data on a scatter plot. It minimizes the distance between the line and all the points.

Front

What is the relationship between x and y in direct variation?

Back

In direct variation, the relationship can be expressed as \( y = kx \), where k is a non-zero constant. This means that as x increases, y increases proportionally.