Test Algebra Mid-Chapter 4 Sections 1-4

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1. Write an equation of a line in slope-intercept form with the given slope and y-intercept.Slope 1/4; y-intercept 3

Explanation

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 1/4 and the y-intercept is 3. Therefore, the equation of the line is y = 1/4x + 3.

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About This Quiz
Test Algebra Mid-Chapter 4 Sections 1-4 - Quiz

This Algebra quiz assesses understanding of linear equations, focusing on writing equations in slope-intercept form. It tests skills in formulating equations from slopes, y-intercepts, and points, crucial for... see morestudents mastering algebraic concepts. see less

2. Write an equation in point slope form, y space minus space y subscript 1 space equals space m left parenthesis x space minus space x subscript 1 right parenthesis, for the line that passes through the point (2, 2) and has the slope -3.

Explanation

The equation y - 2 = -3(x - 2) is the correct answer. It is in point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In this case, the point (2, 2) is on the line and the slope is -3. Plugging in these values into the equation gives y - 2 = -3(x - 2).

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3. Write an equation in slope-intercept form for the graph given.

Explanation

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4. Write the equation y space minus space 3 space equals space minus 5 left parenthesis x space plus space 12 right parenthesis in slope-intercept form, y = mx + b.

Explanation

The equation y = -5x - 57 is in slope-intercept form, y = mx + b, where m is the slope (-5) and b is the y-intercept (-57). This means that the graph of this equation is a straight line with a slope of -5 and crosses the y-axis at -57.

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5. Quadrilateral ABCD has diagonals stack A C with bar on top and stack B D with bar on top. Determine whether stack A C with bar on top is perpendicular to stack B D with bar on top. Explain.

Explanation

The given answer is correct. The slopes of the diagonals are 7 and -7, which are negative reciprocals of each other. In geometry, two lines are perpendicular if and only if their slopes are negative reciprocals of each other. Therefore, the diagonals in quadrilateral ABCD are perpendicular to each other.

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6. Write an equation in slope intercept for the graph given.

Explanation

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7. The cost for 7 dance lessons is $82. The cost or 11 lessons is $122. Write a linear equation to find the total cost for n lessons. Then use the equation to find the cost of 4 lessons.

Explanation

The linear equation to find the total cost C for n lessons is C = 10n + 12. This equation is derived by observing that the cost increases by $10 for each additional lesson, and there is an additional fixed cost of $12.

To find the cost of 4 lessons, we substitute n = 4 into the equation: C = 10(4) + 12 = $40 + $12 = $52. Therefore, the cost of 4 lessons is $52.

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8. Write an equation in point-slope form for the line that passes through the point (-3, -4) with the slope of 0.

Explanation

The equation y + 4 = 0 is the correct answer. In point-slope form, the equation is y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope. In this case, the given point is (-3, -4) and the slope is 0. Plugging in these values into the equation gives us y - (-4) = 0(x - (-3)), which simplifies to y + 4 = 0.

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9. Write an equation of the line that passes through the given point with the given slope.

Explanation

The equation of a line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. In the given equation, y = 3x - 1, the slope is 3. Therefore, the equation y = 3x - 1 represents a line that passes through a given point with a slope of 3.

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10. Write an equation of the line that passes through the given point with the given slope.(-5, 4); slope -3

Explanation

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 given point is (-5, 4) and the slope is -3. Plugging these values into the equation, we get y = -3x - 11. This equation represents a line that passes through the point (-5, 4) and has a slope of -3.

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11. Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the given equation.(-6, -5), 4x + 3y = -6

Explanation

The given equation is in standard form, so we need to rearrange it to slope-intercept form (y = mx + b) to find the slope. We can do this by isolating y: 3y = -4x - 6, y = (-4/3)x - 2. The slope of the given equation is -4/3. Since the line we want to find is perpendicular to this line, the slope of the new line will be the negative reciprocal of -4/3, which is 3/4. Using the point-slope form (y - y1 = m(x - x1)), we can substitute the point (-6, -5) and the slope 3/4 into the equation to get y + 5 = (3/4)(x + 6). Simplifying further, we get y = (3/4)x + 9/2.

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12. Write an equation of the line that passes through each pair of points.(0, -4), (5, -4)

Explanation

The equation y = -4 represents a horizontal line passing through the y-coordinate -4. Since both points (0, -4) and (5, -4) have the same y-coordinate, the line that passes through them will be a horizontal line at y = -4.

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13. Write an equation in slope intercept form for the line that passes through the given point and is parallel to the graph of the given equation.(-3, 4), 3y = 2x - 3

Explanation

To find the equation of a line that is parallel to the given equation, we need to determine the slope of the given line. By rearranging the equation, we can see that the slope of the given line is 2/3. Since the parallel line has the same slope, we can plug in the coordinates of the given point (-3, 4) and the slope (2/3) into the slope-intercept form equation y = mx + b. Solving for b, we find that b = 10/3. Therefore, the equation of the line that passes through (-3, 4) and is parallel to 3y = 2x - 3 is y = (2/3)x + 10/3.

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14. Write the equation y space minus space 11 space equals space 3 left parenthesis x space minus space 2 right parenthesis in standard form, Ax + By = C.

Explanation

The given equation is 3x - y = -5. To write it in standard form, we need to rearrange the terms so that the x and y variables are on the left side and the constant term is on the right side. Therefore, the equation can be written as 3x - y + 5 = 0. This is the standard form, Ax + By = C, where A = 3, B = -1, and C = 5.

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15. Write an equation in slope intercept form for the line that passes through the given point and is parallel to the graph of the given equation.(3, 2), y = x + 5

Explanation

To find an equation in slope-intercept form for a line parallel to y = x + 5, we need to use the same slope. The slope of y = x + 5 is 1. Therefore, the equation of the parallel line will also have a slope of 1. Since the line passes through the point (3, 2), we can use the point-slope form of a linear equation to write the equation as y - 2 = 1(x - 3). Simplifying this equation gives us y - 2 = x - 3. Rearranging the equation to the slope-intercept form, we get y = x - 1.

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16. Carla has already written 10 pages of a novel. She plans to write 15 additional pages per month until she is finished._____ A) Write an equation to find the total number of pages P written after any number of months m. (answer should be in the form P = mm + b)_____ B) Graph the equation on a separate grid. (Type the word GRID in all caps for the answer)_____ C) Find the total number of pages written after 5 months. (Enter the number only)

Explanation

The equation P = 15m + 10 represents the total number of pages written after any number of months. The variable m represents the number of months, and the constant 10 represents the initial 10 pages that Carla has already written. Each month, Carla writes an additional 15 pages, which is represented by the coefficient 15.

The word "GRID" indicates that a graph should be created to represent the equation.

To find the total number of pages written after 5 months, we can substitute m = 5 into the equation: P = 15(5) + 10 = 85. Therefore, the total number of pages written after 5 months is 85.

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17. A construction company charges $15 per hour for debris removal, plus a one-time fee for the use of a trash dumpster. The total fee for 9 hours of service is $195._____ A) Write the point slope form of an equation to find the total fee y for any number of hours x.y space minus space y subscript 1 space equals space m open parentheses x space minus space x subscript 1 close parentheses_____ B) Write the equation in slope intercept form. mx + b_____ C) What is the fee for the use of a trash dumpster. (Enter ONLY a number) 

Explanation

The given equation y - 195 = 15(x - 9) represents the point-slope form of an equation to find the total fee y for any number of hours x. It shows that the total fee y is equal to $15 per hour multiplied by the number of hours x, minus the one-time fee for the use of a trash dumpster, which is $195. The equation y = 15x + 60 is the slope-intercept form of the same equation, where the slope (m) is 15 and the y-intercept (b) is 60. Therefore, the fee for the use of a trash dumpster is $60.

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Write an equation of a line in slope-intercept form with the given...
Write an equation in point slope form, , for the line that passes...
Write an equation in slope-intercept form for the graph given.
Write the equation  in slope-intercept form, y = mx + b.
Quadrilateral ABCD has diagonals  and ....
Write an equation in slope intercept for the graph given.
The cost for 7 dance lessons is $82. The cost or 11 lessons is $122....
Write an equation in point-slope form for the line that passes through...
Write an equation of the line that passes through the given point with...
Write an equation of the line that passes through the given point with...
Write an equation in slope-intercept form for the line that passes...
Write an equation of the line that passes through each pair of...
Write an equation in slope intercept form for the line that passes...
Write the equation  in standard form, Ax + By = C.
Write an equation in slope intercept form for the line that passes...
Carla has already written 10 pages of a novel. She plans to write 15...
A construction company charges $15 per hour for debris removal, plus a...
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