Algebra: Concepts and Connections EOC Review 4

Front

What is the correlation coefficient, r, and how is it interpreted?

Back

The correlation coefficient, r, measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

Front

How do you calculate the constant percent rate of change?

Back

The constant percent rate of change can be calculated using the formula: \( r = \frac{(final\ value - initial\ value)}{initial\ value} \times 100 \% \).

Front

What does it mean for two lines to be parallel in algebra?

Back

Two lines are parallel if they have the same slope and will never intersect. Their equations can be expressed in the form \( y = mx + b \), where m is the slope.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

How do you interpret the solution of a system of inequalities in a real-world context?

Back

The solution of a system of inequalities represents all possible combinations of values that satisfy all inequalities, often visualized as a shaded region on a graph.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0. It is represented as (0, b) in the equation \( y = mx + b \).

Front

How do you determine the maximum or minimum value in a word problem involving constraints?

Back

To determine the maximum or minimum value, set up a function based on the problem's context and use the constraints to find the feasible region. Evaluate the function at the vertices of this region.

Front

What is the formula for the slope of a line given two points?

Back

The slope (m) of a line given two points (x1, y1) and (x2, y2) is calculated as: \( m = \frac{(y2 - y1)}{(x2 - x1)} \).

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be graphically represented as a straight line. It has the form \( y = mx + b \), where m is the slope and b is the y-intercept.

Front

How do you find the equation of a line given a point and a slope?

Back

Use the point-slope form of the equation: \( y - y1 = m(x - x1) \), where (x1, y1) is the point and m is the slope.