Chapter 5 Practice Test

The x-intercept represents the number of quarters needed to park for 60 minutes without using any nickels. In this case, the x-intercept is 2, indicating that 2 quarters are required to park for the full duration.

The equation that describes a line passing through (-6, 8) and is perpendicular to the line y = 2x - 4 is y = -1/2x + 5. This is because the slope of the given line is 2, so the slope of the perpendicular line would be -1/2 (the negative reciprocal). The y-intercept of the perpendicular line can be found by substituting the coordinates of the given point (-6, 8) into the equation.

The equation 5x + 2y = 10 is not a direct variation because it does not represent a relationship where one variable is directly proportional to the other. In a direct variation, the equation would be in the form y = kx, where k is a constant. However, in this equation, there is a constant term (10) and the variables (x and y) are not directly proportional to each other. Therefore, it does not represent a direct variation.

When two lines have the same slope but different y-intercepts, they are parallel to each other. Parallel lines never intersect, as they maintain a constant distance between each other. Therefore, the correct answer is that the lines will never intersect.

The equation of a line can be represented in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -2/3 and the line passes through the point (6, 1). By substituting the values into the equation, we can solve for the y-intercept. Thus, the equation of the line is y = -2/3x + 5.

The formula for Point-Slope Form is y-y1=m(x-x1). This formula represents a linear equation in the form of y = mx + b, where m is the slope of the line and (x1, y1) are the coordinates of a point on the line. By substituting these values into the equation, we can determine the equation of a line given its slope and a point on the line.

The equation of a line perpendicular to y = 3/4x + 1 will have a slope that is the negative reciprocal of 3/4. The negative reciprocal of 3/4 is -4/3. Therefore, the equation of the line perpendicular to y = 3/4x + 1 will be y = -4/3x + b, where b is the y-intercept. To find the value of b, we can substitute the coordinates of the point (3,2) into the equation. Plugging in the values, we get 2 = -4/3(3) + b. Solving for b, we find that b = 6. Therefore, the equation of the line perpendicular to y = 3/4x + 1 through the point (3,2) is y = -4/3x + 6.

The equation y - 5 = 3(x - 7) represents a line in slope-intercept form, where the slope is 3 and the y-intercept is (7, 5). To check if a point lies on this line, we substitute the x and y coordinates of the point into the equation and see if it holds true. For the point (-5, -7), substituting these values into the equation gives -7 - 5 = 3(-5 - 7), which simplifies to -12 = -36. Since this equation is true, the point (-5, -7) lies on the line.

The equation y = 5x - 3 describes the line with a slope of 5 and y-intercept of -3. The slope of 5 indicates that for every increase of 1 in the x-coordinate, the y-coordinate increases by 5. The y-intercept of -3 means that the line crosses the y-axis at the point (0, -3). Therefore, the equation y = 5x - 3 represents a line with a slope of 5 and a y-intercept of -3.

To find the slope of a line passing through two points, we can use the formula: slope = (change in y)/(change in x).

Using the points (1, -1) and (-2, 8), we can calculate the change in y as -1 - 8 = -9, and the change in x as 1 - (-2) = 3.

Therefore, the slope of the line is -9/3 = -3.

The equation of a line can be represented in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -4/7, so the equation starts with y = -4/7x. The line passes through the point (0, -3), which means that when x = 0, y = -3. Plugging these values into the equation, we get -3 = -4/7(0), which simplifies to -3 = 0. Therefore, the y-intercept is -3. Combining the slope and y-intercept, we get the equation y = -4/7x - 3.

The graph of g(x) is obtained by reflecting the graph of f(x) across the y-axis. This means that each point on the graph of f(x) is transformed to a point on the graph of g(x) with the same x-coordinate but opposite y-coordinate. Therefore, the correct answer is a reflection across the y-axis.

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The line y = -(1/4)x + 1 is perpendicular to the line y = 4x + 1 because the slopes of perpendicular lines are negative reciprocals of each other. The slope of y = 4x + 1 is 4, so the slope of the perpendicular line must be -1/4. Additionally, both lines have a y-intercept of 1, which is consistent with the given equation y = -(1/4)x + 1. Therefore, y = -(1/4)x + 1 is the line that is perpendicular to y = 4x + 1.

The domain of a function represents the set of all possible input values for the function. In this case, the function f(x) = 105x represents the cost of renting the home for x days. Since the number of days cannot be negative, the domain of this function would be all positive integers starting from 0. Therefore, the correct answer is (0, 1, 2, 3,...).

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The pair of lines that are parallel are II and IV. This can be determined by comparing the slopes of the lines. The equation of a line can be written in the form y = mx + b, where m is the slope of the line. In equations II and IV, the coefficient of x is the same (-4), indicating that the slopes of these lines are equal. Therefore, II and IV are parallel lines.

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The equation y + 3 = 2(x - 4) describes the line with a slope of 2 that contains the point (4, -3). This equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept. In this equation, the slope is 2 and the point (4, -3) satisfies the equation when plugged in. Therefore, this equation accurately describes the line with the given conditions.

The given line y = 4x + 1 has a slope of 4. In order for a line to be parallel to this line, it must have the same slope of 4. The line y = 4x - 1 has a slope of 4, making it parallel to the given line.

The wage increase at the greatest rate occurred during the time interval of 1990 to 1991.

The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is given as 1/4. The line passes through the point (5, -2), which means that when x = 5, y = -2. Plugging these values into the equation, we get -2 = (1/4)(5) + b. Solving for b, we find that b = -13/4. Therefore, the equation of the line is y = 1/4x - 13/4.

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

Given the points (2,6) and (4,-2), we can calculate the slope as (change in y) / (change in x) = (-2 - 6) / (4 - 2) = -8 / 2 = -4.

Using the point-slope form, we can substitute the values of (x1, y1) = (2, 6) and m = -4 into the equation to get y - 6 = -4(x - 2), which is equivalent to y - 6 = -4x + 8.

Similarly, substituting the values of (x1, y1) = (4, -2) and m = -4, we get y + 2 = -4(x - 4), which is equivalent to y + 2 = -4x + 16.

Therefore, the correct answers are y - 6 = -4(x - 2) and y + 2 = -4(x - 4).