I had an assignment containing 45 problems, and I am unsure of 4, can you check and see if the answers are correct?
1. Write an equation of the line containing the given point and parallel line
(5,-1), 3x-7y=9
My answer was: y=3/7x-22/7
2. Find the equation of the line having the given slope and containing the given point: m=-6,(7,8)
My answer: y=-6x+37
3. Find the slope-intercept of the line that has the given characteristics: slope 8 and y intercept (0,7)My answer was y=8x-7
4. Find an equation of the line containing the given pair of points:(-5,-1)(-9,-7)
I got: y=3/2x+6.5
didn't I just answer this?
Sure, I can help you check the answers for the four problems.
1. To determine if the equation you provided, y = 3/7x - 22/7, is parallel to the given line, you should compare the slopes. The given equation is 3x - 7y = 9. To find the slope, rearrange the equation into slope-intercept form (y = mx + b):
3x - 7y = 9
-7y = -3x + 9
y = (3/7)x - 9/7
The slope of the given line is 3/7. Since the equation you provided also has a slope of 3/7, it is indeed parallel to the given line. Therefore, your answer is correct.
2. You need to find the equation of a line with slope m = -6 and passing through the point (7, 8). The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Plug in the values into the equation:
y = -6x + b
To find b, substitute the x and y values of the given point:
8 = -6(7) + b
8 = -42 + b
b = 8 + 42
b = 50
Therefore, the equation of the line is y = -6x + 50. Your provided answer, y = -6x + 37, is incorrect.
3. You are asked to find the slope-intercept form of a line with a slope of 8 and a y-intercept of (0, 7). The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Simply substitute the given values into the equation:
y = 8x + 7
Therefore, your answer, y = 8x - 7, is incorrect.
4. To find the equation of a line passing through two given points (-5, -1) and (-9, -7), you need to determine the slope first. The formula for slope (m) is (y2 - y1) / (x2 - x1). Let's calculate it using the given points:
m = (-7 - (-1)) / (-9 - (-5))
m = (-7 + 1) / (-9 + 5)
m = -6 / -4
m = 3/2
Now that we have the slope, we can use the point-slope form of a line to find the equation. Using the second point (-9, -7) and the slope (3/2):
y - y1 = m(x - x1)
y - (-7) = (3/2)(x - (-9))
y + 7 = (3/2)(x + 9)
y + 7 = (3/2)x + 27/2
y = (3/2)x + 27/2 - 14/2
y = (3/2)x + 13/2
Therefore, your answer, y = 3/2x + 6.5, is incorrect.
To recap, out of the four provided answers, only your answer to the first problem is correct. The correct answers to the other three problems are:
2. y = -6x + 50
3. y = 8x + 7
4. y = (3/2)x + 13/2