Mastering Linear Equations for GED Quiz

Which graph shows the line 4x - 3y = 12

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Answer explanation

To solve for x in the equation 3x + 5 = 20, subtract 5 from both sides to get 3x = 15. Then, divide both sides by 3 to find x = 5. Thus, the correct answer is x = 5.

Answer explanation

The slope of a line in the equation y = mx + b is represented by the coefficient of x, which is m. In this case, m = 4, so the slope of the line is 4.

Answer explanation

To convert to slope-intercept form, solve for y: 3y = -2x + 6, then y = -\frac{2}{3}x + 2. The correct choice is y = -\frac{2}{3}x + 2.

Answer explanation

The y-intercept of a linear equation in the form y = mx + b is the value of y when x = 0. For the equation y = -2x + 3, when x = 0, y = 3. Therefore, the y-intercept is 3.

Answer explanation

The equation is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Here, the slope is \frac{1}{2} and the y-intercept is -4, making the correct choice: Slope: \frac{1}{2}, y-intercept: -4.

Solve the word problem: If 5 times a number decreased by 3 equals 12, what is the number?

Answer explanation

Let the number be x. The equation is 5x - 3 = 12. Adding 3 to both sides gives 5x = 15. Dividing by 5, we find x = 3. Thus, the number is 3.

Answer explanation

To solve the equations, substitute y from the first equation into the second: x - (10 - x) = 2. This simplifies to 2x - 10 = 2, leading to 2x = 12, so x = 6. Then, y = 10 - 6 = 4. Thus, the solution is (6, 4).

Answer explanation

To solve for x in the equation 4x - 7 = 9, add 7 to both sides to get 4x = 16. Then, divide both sides by 4 to find x = 4. Thus, the correct answer is x = 4.

Write a linear expression to represent the context: "The total cost is 5 times the number of items plus a fixed fee of $10."

Answer explanation

The expression "5x + 10" represents the total cost, where "5x" accounts for the cost of 5 times the number of items (x) and "10" is the fixed fee. This matches the context given in the question.