2024 fall exam review

Front

What is the formula to calculate the slope of a line?

Back

The slope (m) of a line is calculated using the formula: m = \frac{y_2 - y_1}{x_2 - x_1}.

Front

Calculate the slope of the line through the points (6,1) and (8,7).

Back

The slope is 3.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b^x), where a is a constant, b is the base, and x is the exponent.

Front

Write the equation of the exponential function for the given graph if it passes through (0,1) and has a base of 4.

Back

y = 1(4)^x.

Front

What is a determinant in a matrix?

Back

The determinant is a scalar value that is a function of the entries of a square matrix and provides important properties of the matrix.

Front

How do you evaluate the determinant of a 2x2 matrix?

Back

For a 2x2 matrix \begin{pmatrix} a & b \\ c & d \end{pmatrix}, the determinant is calculated as ad - bc.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as one variable increases, the other variable also increases.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as one variable increases, the other variable decreases.

Front

How do you find the slope of a line given two points?

Back

Use the formula m = \frac{y_2 - y_1}{x_2 - x_1} with the coordinates of the two points.