Praxis Core Math Linear Equations and Functions Quiz

To find the x-intercept of the equation y = 3x - 9, set y to 0 and solve for x. This gives 0 = 3x - 9. Adding 9 to both sides results in 3x = 9, and dividing by 3 yields x = 3. Thus, the x-intercept is 3.

Perpendicular lines have slopes that are negative reciprocals of each other. If one line has a slope of 2, the negative reciprocal is calculated as -1/2. Therefore, the slope of the other line is -0.5.

To solve the equation 4x + 6 = 2x + 18, first, isolate x by subtracting 2x from both sides, resulting in 2x + 6 = 18. Next, subtract 6 from both sides to get 2x = 12. Finally, divide by 2, yielding x = 6.

The domain of the linear function f(x) = 5x + 2 encompasses all real numbers because linear functions are defined for every value of x. There are no restrictions such as division by zero or square roots of negative numbers, allowing any real number input.

To solve the equation 3x + 7 = 22, first subtract 7 from both sides, resulting in 3x = 15. Then, divide both sides by 3 to isolate x, yielding x = 5. This value satisfies the original equation, confirming it as the correct solution.

To find the slope of the line through points (2, 5) and (4, 9), use the formula \((y_2 - y_1) / (x_2 - x_1)\). Here, \(y_2 = 9\), \(y_1 = 5\), \(x_2 = 4\), and \(x_1 = 2\). This gives \((9 - 5) / (4 - 2) = 4 / 2 = 2\). Thus, the slope is 2.

A linear function is defined by an equation of the form y = mx + b, where m and b are constants. The equation y = 2x + 3 fits this format, representing a straight line with a slope of 2 and a y-intercept of 3. The other options involve non-linear expressions.

To find the y-intercept of the line represented by the equation 2x + 3y = 12, set x to 0. This gives 3y = 12, leading to y = 4. Thus, the y-intercept, where the line crosses the y-axis, is 4.

To solve the equation 5x - 2 = 3x + 8, first isolate x by moving 3x to the left side and 2 to the right side. This simplifies to 2x = 10. Dividing both sides by 2 gives x = 5, which is the solution to the equation.

A horizontal line has a constant y-value regardless of changes in x, meaning there is no vertical change as you move along the line. Since slope is calculated as the change in y divided by the change in x, and there is no change in y, the slope is 0.

To find f(3), substitute 3 into the function f(x) = 4x - 5. This gives f(3) = 4(3) - 5 = 12 - 5 = 7. Therefore, the value of f(3) is 7.

To solve the equation 2(x + 3) = 16, first divide both sides by 2, yielding x + 3 = 8. Next, subtract 3 from both sides to isolate x, resulting in x = 5. This solution satisfies the original equation, confirming its correctness.