Exam Review Part 1 (covers questions 1-10 on exam study guide)

Front

What does it mean when an absolute value equation has no solution?

Back

An absolute value equation has no solution when the expression inside the absolute value cannot equal the negative value on the other side of the equation.

Front

Solve the equation: |x + 3| = 2. What are the solutions?

Back

x + 3 = 2 or x + 3 = -2; Solutions: x = -1 or x = -5.

Front

What are x and y intercepts in a graph?

Back

The x-intercept is the point where the graph crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0).

Front

How do you find the x-intercept of the equation 2x + 4y = 12?

Back

Set y = 0 and solve for x: 2x + 4(0) = 12; x = 6. The x-intercept is (6, 0).

Front

How do you find the y-intercept of the equation 2x + 4y = 12?

Back

Set x = 0 and solve for y: 2(0) + 4y = 12; y = 3. The y-intercept is (0, 3).

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

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the solution set of an equation?

Back

The solution set is the set of all values that satisfy the equation.

Front

What does it mean to graph a solution set?

Back

Graphing a solution set means plotting all the points that satisfy the equation on a coordinate plane.

Front

What is the significance of the absolute value in equations?

Back

Absolute value measures the distance of a number from zero on the number line, regardless of direction.