2024 Semester Review Part I

Front

Graph the equation: 3x - 6y = 12

Back

To graph the equation, first rewrite it in slope-intercept form (y = mx + b). The equation can be rearranged to y = 0.5x - 2. The slope (m) is 0.5 and the y-intercept (b) is -2.

Front

What does the inequality y > 4x - 1 represent graphically?

Back

This inequality represents the region above the line y = 4x - 1. The line itself is not included in the solution set.

Front

What does the inequality y < 4x - 1 represent graphically?

Back

This inequality represents the region below the line y = 4x - 1. The line itself is not included in the solution set.

Front

Solve the equation algebraically: |3x + 5| = 1

Back

The solutions are x = -4/3 and x = -2.

Front

What is the x-intercept of the equation 4x - 3y = 24?

Back

To find the x-intercept, set y = 0. The x-intercept is (6, 0).

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 find the y-intercept of a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What does the inequality y < -1/2x + 3 represent graphically?

Back

This inequality represents the region below the line y = -1/2x + 3. The line itself is not included in the solution set.

Front

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

Back

The x-intercept is the point where the line crosses the x-axis, indicating the value of x when y = 0.

Front

How do you solve absolute value equations?

Back

To solve an absolute value equation, set up two separate equations: one for the positive case and one for the negative case.