Final Exam Review

Front

What is the equation of a line given a slope and a point?

Back

The equation of a line can be expressed in the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. To find b, substitute the coordinates of the given point into the equation.

Front

How do you represent a system of equations from a word problem?

Back

Identify the variables, then translate the relationships and conditions described in the problem into equations. Each condition typically corresponds to one equation.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts. This means they will never intersect.

Front

How do you find the slope of a line from a graph?

Back

The slope (m) is calculated as the rise over run, or the change in y divided by the change in x between two points on the line.

Front

What is an inequality in mathematical terms?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert a standard form equation to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

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, representing the value of y when x = 0.

Front

How do you determine if a point lies on a line given its equation?

Back

Substitute the x-coordinate of the point into the equation and see if the resulting y-value matches the y-coordinate of the point.

Front

What is the graphical representation of a linear inequality?

Back

A linear inequality can be represented on a graph by shading one side of the line, indicating all the solutions that satisfy the inequality.