Linear Equations Quiz

1. What value of x satisfies the equation x + 4 = 12?

6

8

16

4

Solving the equation x + 4 = 12 involves isolating x. Subtract 4 from both sides to keep the equation balanced: x + 4 - 4 = 12 - 4, which simplifies to x = 8. This type of problem showcases simple linear equations where the goal is to find the value of x that makes the equation true.

Explanation

Solving the equation x + 4 = 12 involves isolating x. Subtract 4 from both sides to keep the equation balanced: x + 4 - 4 = 12 - 4, which simplifies to x = 8. This type of problem showcases simple linear equations where the goal is to find the value of x that makes the equation true.

2. If y = 2x and x = 3, what is y?

5

6

9

8

The equation y = 2x shows a direct relationship between x and y. When x is 3, substituting it into the equation gives y = 2 * 3. This simplifies to y = 6. Therefore, when x equals 3, y equals 6. This demonstrates a linear relationship where y is always twice the value of x.

Explanation

The equation y = 2x shows a direct relationship between x and y. When x is 3, substituting it into the equation gives y = 2 * 3. This simplifies to y = 6. Therefore, when x equals 3, y equals 6. This demonstrates a linear relationship where y is always twice the value of x.

3. What is the solution to the equation 7x + 2 = 23?

X = 3

X = 21

X = 25

X = 7

Solving the equation 7x + 2 = 23 for x involves isolating x. First, subtract 2 from both sides: 7x + 2 - 2 = 23 - 2, which simplifies to 7x = 21. Then, divide both sides by 7: 7x / 7 = 21 / 7, resulting in x = 3. This process illustrates solving basic linear equations and emphasizes the steps to isolate the variable.

Explanation

Solving the equation 7x + 2 = 23 for x involves isolating x. First, subtract 2 from both sides: 7x + 2 - 2 = 23 - 2, which simplifies to 7x = 21. Then, divide both sides by 7: 7x / 7 = 21 / 7, resulting in x = 3. This process illustrates solving basic linear equations and emphasizes the steps to isolate the variable.

4. For the equation 2x + 6 = y, what is y when x = 4?

14

10

8

12

For the equation 2x + 6 = y, determine y when x = 4 by substituting 4 for x: y = 2(4) + 6 = 8 + 6 = 14. This example demonstrates the direct impact of changes in x on y, highlighting the linear relationship between these variables. In this equation, every unit increase in x results in a doubling effect on the y-value, plus a constant addition of 6. This linear relationship, where y increases consistently as x increases, exemplifies the fundamental algebraic principle of direct variation between dependent and independent variables.

Explanation

For the equation 2x + 6 = y, determine y when x = 4 by substituting 4 for x: y = 2(4) + 6 = 8 + 6 = 14. This example demonstrates the direct impact of changes in x on y, highlighting the linear relationship between these variables. In this equation, every unit increase in x results in a doubling effect on the y-value, plus a constant addition of 6. This linear relationship, where y increases consistently as x increases, exemplifies the fundamental algebraic principle of direct variation between dependent and independent variables.

5. What does x equal in the equation 3x - 9 = 15?

8

5

12

6

Solving the equation 3x - 9 = 15 for x requires isolating x. First, add 9 to both sides to eliminate the -9: 3x - 9 + 9 = 15 + 9, which simplifies to 3x = 24. Then, divide both sides by 3 to solve for x: 3x / 3 = 24 / 3, resulting in x = 8. This type of manipulation is typical in algebra, emphasizing operations that maintain the balance of the equation.

Explanation

Solving the equation 3x - 9 = 15 for x requires isolating x. First, add 9 to both sides to eliminate the -9: 3x - 9 + 9 = 15 + 9, which simplifies to 3x = 24. Then, divide both sides by 3 to solve for x: 3x / 3 = 24 / 3, resulting in x = 8. This type of manipulation is typical in algebra, emphasizing operations that maintain the balance of the equation.

6. Which equation represents a line with slope 3 and y-intercept -1?

Y = 3x - 1

Y = 3x + 1

Y = -1x + 3

Y = 1x - 3

The equation y = 3x - 1 represents a line with a slope of 3 and a y-intercept of -1. Here, 3 is the slope, indicating how much y increases for each one-unit increase in x. The y-intercept -1 is where the line crosses the y-axis. This equation effectively combines these elements to describe the line’s behavior on a graph.

Explanation

The equation y = 3x - 1 represents a line with a slope of 3 and a y-intercept of -1. Here, 3 is the slope, indicating how much y increases for each one-unit increase in x. The y-intercept -1 is where the line crosses the y-axis. This equation effectively combines these elements to describe the line’s behavior on a graph.

7. If y = -2x + 5 and x = -2, what is y?

9

1

0

3

To find y when y = -2x + 5 and x = -2, substitute -2 for x: y = -2(-2) + 5 = 4 + 5 = 9. This demonstrates how to manipulate equations to find y based on given values of x, especially in equations that involve negative coefficients and their effects on the dependent variable.

Explanation

To find y when y = -2x + 5 and x = -2, substitute -2 for x: y = -2(-2) + 5 = 4 + 5 = 9. This demonstrates how to manipulate equations to find y based on given values of x, especially in equations that involve negative coefficients and their effects on the dependent variable.

8. What is the slope of a line with the equation y = 5x + 3?

5

3

0

-5

The slope of the line y = 5x + 3 is determined by the coefficient of x, which is 5. This coefficient represents the rate of change of y with respect to x. In simpler terms, for every increase of one unit in x, y increases by 5 units. This relationship between x and y is fundamental to understanding linear equations, where the slope indicates the steepness and direction of the line on a graph.

Explanation

The slope of the line y = 5x + 3 is determined by the coefficient of x, which is 5. This coefficient represents the rate of change of y with respect to x. In simpler terms, for every increase of one unit in x, y increases by 5 units. This relationship between x and y is fundamental to understanding linear equations, where the slope indicates the steepness and direction of the line on a graph.

9. What is the y-intercept of y = -3x + 7?

3

7

-3

0

The y-intercept of the equation y = -3x + 7 is 7. This value represents the point where the line crosses the y-axis on a graph. The y-intercept is isolated from the x-components of the equation, indicating where the output value of y will be when x equals zero.

Explanation

The y-intercept of the equation y = -3x + 7 is 7. This value represents the point where the line crosses the y-axis on a graph. The y-intercept is isolated from the x-components of the equation, indicating where the output value of y will be when x equals zero.

10. If the equation of a line is y = 4x - 8, what is the y-intercept?

-4

8

4

-8

In the equation y = 4x - 8, the y-intercept is identified as the constant term, which is -8. This term represents where the line intersects the y-axis when x is zero, providing a fixed point on the graph from which the line will extend based on the slope, which in this case is 4.

Explanation

In the equation y = 4x - 8, the y-intercept is identified as the constant term, which is -8. This term represents where the line intersects the y-axis when x is zero, providing a fixed point on the graph from which the line will extend based on the slope, which in this case is 4.