Can someone check my answers?
1. Write the equation of the line that passes through point (–2, 3) with a slope of –4.
Answer: y = -4x - 5
2. Find the slope and y-intercept.
x = –8
Answer: Slope: undefined; y-intercept: none
3. Write the equation of the line which has y-intercept (0, 5) and is perpendicular to the line with equation y = –3x + 1.
Answer: y = 1/3x + 5
4. Write the equation of the line passing through (4, 4) and (4, 2).
Answer: x = 4
5. Determine which two equations represent perpendicular lines.
A. y = 4/7x – 3
B. y = 3x – 4/7
C. y = -1/3x + 4/7
D. y = 1/3x – 4/7
Answer: b and c
6. Find the y-intercept.
–x + 3y = 15
Answer: (0,5)
7. Determine which two equations represent parallel lines.
A. y = 5/3x + 4
B. y = -3/5x – 7
C. y = 2x + 8
D. y = 2x – 4
Answer: c and d
8. Find the slope of the line passing through the points (–7, –4) and (–1, –10).
Answer: -1
9. Find the slope of the line passing through the points (–9, –4) and (0, –4).
Answer: 0
10. Find the slope of the line passing through the points (4, 0) and (4, 5).
Answer: Undefined
11. An employee who produces x units per hour earns an hourly wage of y = 0.35x + 11 (in dollars). Find the hourly wage for an employee who produces 2 units per hour.
Answer: $11.70
12. Which of the ordered pairs
(3, 1), (0, –4), (–4, 0), (–3, –7)
are solutions for the equation x – y = 4?
Answer: (0, –4) and (–3, –7)
13. Find the slope of the line passing through the points (–8, –3) and (–2, 2).
Answer: 5/6
#1 correct
#2 you did not finish writing the question
5,-2 -3.8
10) Two perpendicular lines pass through the point (0, -8). One of the lines has a slope of -4. Write the equation of both lines in slope-intercept form.
To check your answers, let's go through each question one by one.
1. To find the equation of a line passing through a given point with a given slope, you can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the given slope. In this case, the point is (-2, 3) and the slope is -4. Plugging in these values into the equation, we have y - 3 = -4(x - (-2)). Simplifying it further, we get y - 3 = -4(x + 2). Expanding the equation, we get y - 3 = -4x - 8. Finally, solving for y, we have y = -4x - 5. Therefore, your answer is correct.
2. To find the slope and y-intercept of a line represented by the equation in the form y = mx + b, the coefficient of x is the slope (m) and the constant term is the y-intercept (b). In this case, the equation is x = -8. Since x is not multiplied by any coefficient, the slope is undefined. Also, there is no constant term for y, so there is no y-intercept. Therefore, your answer is correct.
3. To find the equation of a line perpendicular to a given line, you need to find the negative reciprocal of the given line's slope. The given line has the equation y = -3x + 1, which means the slope is -3. The negative reciprocal of -3 is 1/3. Since the line has a y-intercept of (0, 5), the equation in slope-intercept form becomes y = 1/3x + 5. Therefore, your answer is correct.
4. To find the equation of a line passing through two given points, you can use the point-slope form. The two points given are (4, 4) and (4, 2). Since the x-coordinate is the same for both points, the line is vertical and the equation will be of the form x = a, where a is the x-coordinate. In this case, the x-coordinate is 4. Therefore, your answer is correct.
5. To determine which equations represent perpendicular lines, you need to find the slopes of each equation. Perpendicular lines have slopes that are negative reciprocals of each other. The equations are:
A. y = 4/7x - 3 (slope = 4/7)
B. y = 3x - 4/7 (slope = 3)
C. y = -1/3x + 4/7 (slope = -1/3)
D. y = 1/3x - 4/7 (slope = 1/3)
Comparing the slopes, you can see that the slope of line B is the negative reciprocal of the slope of line C. Therefore, lines B and C are perpendicular. Therefore, your answer is correct.
6. To find the y-intercept of a line represented by an equation in the form Ax + By = C, you can simply set x = 0 and solve for y. In this case, the equation is -x + 3y = 15. Setting x = 0, we have -0 + 3y = 15, which simplifies to 3y = 15. Dividing both sides by 3, we get y = 5. Therefore, the y-intercept is (0, 5). Therefore, your answer is correct.
7. To determine which equations represent parallel lines, you need to compare their slopes. Parallel lines have the same slope. The equations are:
A. y = 5/3x + 4 (slope = 5/3)
B. y = -3/5x - 7 (slope = -3/5)
C. y = 2x + 8 (slope = 2)
D. y = 2x - 4 (slope = 2)
Comparing the slopes, you can see that lines C and D have the same slope. Therefore, lines C and D are parallel. Therefore, your answer is correct.
8. To find the slope of a line passing through two points, you can use the formula: slope = (y2 - y1) / (x2 - x1). The two points given are (-7, -4) and (-1, -10). Plugging the values into the formula, we have slope = (-10 - (-4)) / (-1 - (-7)). Simplifying it further, we get slope = -6 / 6 = -1. Therefore, your answer is correct.
9. To find the slope of a line passing through two points, you can use the formula: slope = (y2 - y1) / (x2 - x1). The two points given are (-9, -4) and (0, -4). Plugging the values into the formula, we have slope = (-4 - (-4)) / (0 - (-9)). Simplifying it further, we get slope = 0 / 9 = 0. Therefore, your answer is correct.
10. To find the slope of a line passing through two points, you can use the formula: slope = (y2 - y1) / (x2 - x1). The two points given are (4, 0) and (4, 5). Plugging the values into the formula, we have slope = (5 - 0) / (4 - 4). Simplifying it further, we get slope = 5 / 0. However, division by 0 is undefined. Therefore, the slope is undefined. Therefore, your answer is correct.
11. To find the hourly wage for an employee who produces a certain number of units per hour, you can substitute the given number of units (x) into the wage formula y = 0.35x + 11. In this case, the given number of units is 2. Plugging in the value into the formula, we have y = 0.35 * 2 + 11. Simplifying it further, we get y = 0.70 + 11 = 11.70. Therefore, the hourly wage for an employee who produces 2 units per hour is $11.70. Therefore, your answer is correct.
12. To check which ordered pairs are solutions for a given equation, you can substitute the x and y values of each pair into the equation and see if it satisfies the equation. In this case, the equation is x - y = 4. Checking each pair:
- For (3, 1): 3 - 1 = 4. This does not satisfy the equation.
- For (0, -4): 0 - (-4) = 4. This satisfies the equation.
- For (-4, 0): -4 - 0 = 4. This does not satisfy the equation.
- For (-3, -7): -3 - (-7) = 4. This satisfies the equation.
Therefore, the solutions for the equation x - y = 4 are (0, -4) and (-3, -7). Therefore, your answer is correct.
13. To find the slope of a line passing through two points, you can use the formula: slope = (y2 - y1) / (x2 - x1). The two points given are (-8, -3) and (-2, 2). Plugging the values into the formula, we have slope = (2 - (-3)) / (-2 - (-8)). Simplifying it further, we get slope = 5 / 6. Therefore, the slope of the line passing through the points (-8, -3) and (-2, 2) is 5/6. Therefore, your answer is correct.
Overall, your answers are correct for all the questions. Well done! If you have any more questions, feel free to ask.