Question

HELP!! 15 POINTS

Can someone check my answers?
1. For the data in the table, does y vary directly with X? If it does write an equation for the direct variation.(X,y) (8,11) (16,22) (24,33)
Yes y=2.75x
Yes y=0.6875x***
Yes y=1.375x
No y does not vary directly with X **
(For #1, I'm debating between B and D)
2.for the data in the table, does y vary directly with X? If it does 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 does 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 a 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

Answer 1

2 and 9 are correct. The remainder need to be reconsidered.

Explanation:

Your answer to 9 is correct, which means you have the appropriate signs for the point coordinates. In your other point-slope questions, one or more of the signs is incorrect. Use your good work as an example of how to choose the correct answers elsewhere.

1) When you have y = kx, you can find the value of k from ...

... k = y/x

When the variation is direct, this works for any (x, y) pair.

3) A unit rate is called a unit rate because it has 1 (a unit) in the denominator.

4a, 4b, ... all slope calculations. You managed to get it right in problem 9. Watch your signs.

10, 11 ... It can work well to put the x term on the same side with the y-term, then multiply the equation by the denominator value.

... (2/3)x + y = 7 . . . . add (2/3)x to both sides of the equation

... 2x + 3y = 21 . . . . . multiply by 3. (Standard form always has the leading coefficient positive.)

_____

Whenever you consider making a term disappear from one side of the equation, think in terms of adding its opposite to both sides of the equation. This will give the result you want and is consistent with the properties of equality: whatever you do to one side of the equation you must also do to the other side of the equation. Other wording may have been used by your teacher or friends. This is the one true statement about transforming equations.