2.on which of the following lines does the point (7, 1) lie
A. y - 5x = 4
B.y = x - 10
C. y=-4x + 3
D. y= -x + 8
Is it B?
3.Find the slope of the line through (-9, -10) & (-2, -5)
A -5/7
B 7/5
C 5/7
D -7/5
Is it D?
10. The equation t=0.07c represents tax, t , based on the cost, c, of an item. which part of the equation represents the constant of proportionality?
A. t
B. 0.07
C. c
D. 7
Is it B?
#2 I'd say B is wrong, since 7-10 ≠ 1
#3 The slope is (-5+10)/(-2+9) ≠ -7/5
#10 correct
To determine on which line the point (7, 1) lies, we need to substitute the x and y coordinates of the point into each of the given equations and check if the equation is satisfied.
A. y - 5x = 4: Substitute x = 7 and y = 1
1 - 5(7) ≠ 4
-34 ≠ 4
B. y = x - 10: Substitute x = 7 and y = 1
1 = 7 - 10
1 = -3 (Not satisfied)
C. y = -4x + 3: Substitute x = 7 and y = 1
1 = -4(7) + 3
1 = -28 + 3
1 = -25 (Not satisfied)
D. y = -x + 8: Substitute x = 7 and y = 1
1 = -7 + 8
1 = 1 (Satisfied)
Therefore, the point (7, 1) lies on line D, which is represented by the equation y = -x + 8. So, yes, the answer is B.
To find the slope of the line passing through (-9, -10) and (-2, -5), you can use the formula for slope, which is given by:
slope (m) = (change in y) / (change in x)
Substituting the coordinates into the formula, we get:
m = (-5 - (-10)) / (-2 - (-9))
m = (-5 + 10) / (-2 + 9)
m = 5 / 7
Thus, the slope of the line passing through (-9, -10) and (-2, -5) is 5/7. So, no, the answer is not D. The correct answer is C.
In the equation t = 0.07c, t represents the tax, c represents the cost of an item, and 0.07 represents the constant of proportionality. So, the answer is not B. The correct answer is B.
2. To determine on which line the point (7, 1) lies, you need to substitute the x and y coordinates of the point into the equations to see which one is satisfied. Let's check each option:
A. y - 5x = 4
Substituting x = 7 and y = 1: 1 - 5(7) = 1 - 35 = -34 ≠ 4, so the point does not lie on this line.
B. y = x - 10
Substituting x = 7 and y = 1: 1 = 7 - 10 = -3 ≠ 1, so the point does not lie on this line.
C. y = -4x + 3
Substituting x = 7 and y = 1: 1 = -4(7) + 3 = -28 + 3 = -25 ≠ 1, so the point does not lie on this line.
D. y = -x + 8
Substituting x = 7 and y = 1: 1 = -7 + 8 = 1, which is true. Therefore, the point (7, 1) lies on this line.
So, the correct answer is D.
3. To find the slope of the line through (-9, -10) and (-2, -5), you can use the slope formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given values:
m = (-5 - (-10)) / (-2 - (-9)) = (-5 + 10) / (-2 + 9) = 5 / 7
So, the slope of the line is 5/7.
The correct answer is C.
10. In the equation t = 0.07c, t represents the tax, and c represents the cost of an item. The constant of proportionality is the number that goes in front of the variable, which is 0.07 in this equation.
So, the constant of proportionality is 0.07.
The correct answer is B.