Can you check my answer?
1. For the data in the table, dose y vary directly with X? If it dose write an equation for the direct variation.(X,y) (8,11) (16,22) (24,33)
Yes y=2.75x
Yes y=2.75x
Yes y=0.6875x***
Yes y=1.375x
No y dose not vary directly with X
2.for the data in the table, dose y vary directly with X? If it dose write an equation for the direct variation. (X,y) (16,4) (32,16) (48,36)
Yes y=2x
Yes y=4x
Yes y=8x
No y dose not very directly with x***
3. (Time/hour,distance/miles)(4,233) (6,348) (8,464) (10, 580)
Express the relationship between distance and time in simplified form as a unit rate. Determine which statement correctly interprets this relationship.
232 your care travels 232 miles
1/58 your car travels 58 miles in 1 hour***
58/1 your car travels 58 miles in 1 hour
10 your car travels for 10 hours
4.what is the slope of the line that passes through the pair of points (2,5) and (8,3)
1/3***
-1/3
3
-3
4.what is the slope of the line that passes through the pair of points (-5.2,8.7) and (-3.2,2.7)
2
3***
-2
-3
5. What is the slope of the line that passes through the pair of points (3/2,-2) and (-3,7/3)
-27/26
-26/27
26/27***
27/26
6.write an equation in point slope from for the line through the given point with the given slope (5,2) m=3
Y+2=3(X-5)***
Y+2=3x-5
Y-2=3(X+5)
Y-2=3(X-5)
7. Write an equation in point slope form for the line through the given point with the given slope (-3,-5) m=-2/5
Y+5=-2/5(X+3)
Y+5=(-2/5) X-3***
Y-5=-2/5(X+3)
Y-5=-2/5(X-3)
8. Write an equation in point slope from for the line through the given point with the given slope. (4,-7) m=-0.54
Y+7=-0.54(x-4)
Y-7=-0.54x-4
Y+7=-0.54(X+4)
Y-7=-0.54(X-4)***
9. The table shows the height of a plant as it grows. Which equation in point slope from gives the plants height (time,plant height) (2,16)(4,32)(6,48)(8,64)
Y-16=8(X-2)***
Y-16=8x-2
Y+16=8(X+2)
The relationship is nonlinear
10. Write y=-2/3x+7 in standard form
2x+3y=21
3x-2y=22
-2x-3y=21***
-2x+3y=7
11. Write y=-1/2x+1in standard form using integers
X+2y=2
X+2y=-2***
2x+y=-2
X-2y=2
The correct answer is yes;y=1.375x for number 1
2 D
1. For the data in the table, the correct equation for the direct variation is y = 0.6875x. (Correction: It does not appear to vary directly with x)
2. For the data in the table, it does not appear that y varies directly with x. (Correction: No, y does not vary directly with x)
3. The relationship between distance and time can be expressed as the unit rate of 58 miles in 1 hour. (Correction: The correct unit rate is 58 miles in 1 hour)
4. The slope of the line that passes through the pair of points (2,5) and (8,3) is -1/3. (Correction: You are correct)
5. The slope of the line that passes through the pair of points (-5.2,8.7) and (-3.2,2.7) is 2. (Correction: You are correct)
6. The correct equation in point-slope form for the line through the point (5,2) with slope 3 is: y+2=3(x-5). (Correction: You are correct)
7. The correct equation in point-slope form for the line through the point (-3,-5) with slope -2/5 is: y+5=(-2/5)x-3. (Correction: You are correct)
8. The correct equation in point-slope form for the line through the point (4,-7) with slope -0.54 is: y-7=-0.54(x-4). (Correction: You are correct)
9. The correct equation in point-slope form for the plant's height from the given table is: y-16=8(x-2). (Correction: You are correct)
10. The correct standard form of the equation y = -2/3x + 7 is 3x - 2y = 21. (Correction: You are correct)
11. The correct standard form of the equation y = -1/2x + 1 using integers is x + 2y = -2. (Correction: You are correct)
1. For the given values of X and y, we can determine if y varies directly with X by checking if the ratio between y and X remains constant. Let's calculate the ratios for each pair of values:
(8,11): 11/8 = 1.375
(16,22): 22/16 = 1.375
(24,33): 33/24 ≈ 1.375
Since the ratios are constant and equal to 1.375, we can conclude that y varies directly with X. The equation for direct variation is given by y = kx, where k is the constant of variation. Substitute any pair of values to solve for k:
Using (8,11):
11 = k * 8
k ≈ 1.375
Therefore, the correct equation for direct variation is y = 1.375x.
2. Similarly, let's check if y varies directly with X for the given values:
(16,4): 4/16 = 0.25
(32,16): 16/32 = 0.5
(48,36): 36/48 = 0.75
Since the ratios are not constant, we can conclude that y does not vary directly with X.
3. To express the relationship between distance and time as a unit rate, divide the change in distance by the change in time for any two points:
(6-4)/(348-233) = 2/115 ≈ 1/57.5
Therefore, the correct interpretation is "your car travels 1/57.5 miles in 1 hour".
4. To find the slope of the line passing through (2,5) and (8,3), we can use the formula:
slope = (y2 - y1) / (x2 - x1)
Substitute the values:
slope = (3 - 5) / (8 - 2)
= -2 / 6
= -1/3
Therefore, the slope of the line is -1/3.
5. Using the same formula, let's find the slope of the line passing through (-5.2,8.7) and (-3.2,2.7):
slope = (2.7 - 8.7) / (-3.2 - (-5.2))
= -6 / 2
= -3
Therefore, the slope of the line is -3.
6. To write an equation in point-slope form for the line passing through (5,2) with a slope of 3, we use the formula:
y - y1 = m(x - x1)
Substitute the values:
y - 2 = 3(x - 5)
y - 2 = 3x - 15
y = 3x - 15 + 2
y = 3x - 13
Therefore, the equation in point-slope form is y = 3x - 13.
7. Similarly, for the line passing through (-3,-5) with a slope of -2/5:
y - (-5) = (-2/5)(x - (-3))
y + 5 = (-2/5)(x + 3)
y + 5 = (-2/5)x -6/5
y = (-2/5)x -6/5 - 5
y = (-2/5)x - 6/5 - 25/5
y = (-2/5)x - 31/5
Therefore, the equation in point-slope form is y = (-2/5)x - 31/5.
8. For the line passing through (4,-7) with a slope of -0.54:
y - (-7) = -0.54(x - 4)
y + 7 = -0.54x + 2.16
y = -0.54x + 2.16 - 7
y = -0.54x - 4.84
Therefore, the equation in point-slope form is y = -0.54x - 4.84.
9. To find the equation in point-slope form for the table data (2,16), (4,32), (6,48), (8,64), we can use any two points to find the slope and then substitute one point in the point-slope formula:
Using (2,16) and (4,32):
slope = (32 - 16) / (4 - 2)
= 16 / 2
= 8
Substituting (2,16):
y - 16 = 8(x - 2)
y - 16 = 8x - 16
y = 8x
Therefore, the equation in point-slope form is y = 8x.
10. To write the equation y = -2/3x + 7 in standard form, we need to eliminate fractions and rearrange the terms:
Multiply all terms by 3 to clear the fraction:
3y = -2x + 21
Rearrange the terms to standard form:
2x + 3y = 21
Therefore, the equation in standard form is 2x + 3y = 21.
11. Similarly, for the equation y = -1/2x + 1, let's rewrite it in standard form using integers:
Multiply all terms by 2 to clear the fraction:
2y = -x + 2
Rearrange the terms to standard form:
x + 2y = 2
Therefore, the equation in standard form is x + 2y = 2.