12. the table shows the height of a plant as it grows. which equation in point-slope form gives the plant's height at any time (1 point) time (months) | plant height (cm) 2 | 16 4 | 32 6 | 48 8 | 64 (a). y - 16 = 8(x - 2) (b). y - 16 = 8x - 2 (c). y + 16 = 8(x + 2) (d). the relationship is nonlinear 14. write y = (-5/8)x + 3 in standard form using integers (1 point) (a). 5x + 8y = -24 (b). 5x + 8y = 24 (c). 5x - 8y = 24 (d). -5x + 8y = 24 15. write an equation for the line that is parallel to the given line and passes through the given point (1 point) y = 3x + 7; (2, 10) (a). y = 3x + 11 (b). y = 3x + 4 (c). y = -3x + 4 (d). y = (-1/3)x + 4 16. tell whether the lines for each pair of equations are parallel, perpendicular, or neither (1 point) y = -2x + 4 -5x + 10y = 5 (a). parallel (b). perpendicular (c). neither 17. tell whether the lines for each pair of equations are parallel, perpendicular, or neither (1 point) y = -1/4x + 10 -2x + 8y = 6 (a). parallel (b). perpendicular (c). neither 18. write the equation of a line that is perpendicular to the given line and that passes through the given point (1 point) y - 4 = 5/2 (x + 3); (-7, 8) (a). y - 8 = -2/5 (x - 7) (b). y - 8 = 2/5 (x - 7) (c). y - 8 = -2/5 (x + 7) (d). y - 8 = 2/5 (x + 7)

Ques 12)

Time (months) | Plant Height (cm)

              2 | 16

              4 | 32

              6 | 48

              8 | 64

Now, we see that the line will pass through (2,16) and (4,32)

Now, the equation of line passing through (a,b) and (c,d) is given by:

Here (a,b)=(2,16) and (c,d)=(4,32)

Hence, the equation of line is:

The relationship is clearly linear since we can relate them as:

y=8x

Hence, option: A is correct:

(A). y - 16 = 8(x - 2)

Ques 14)

y = (-5/8)x + 3

In standard form it is:

Hence, option: B is correct.

Ques 15)

y = 3x + 7; (2, 10)

As the line is parallel hence the slope must be same. (i.e. slope of the line y=mx+c is m.

So, here slope=3)

Now,

The line also passes through (2,10).

Hence, the equation is:

y=3x+4

( since, when x=2

y=3×2+4=6+4=10)

Ques 16)

y = -2x + 4 -------------(1)

-5x + 10y = 5-------------(2)

On solving second equation we have:

slope of first line (m)= -2

slope of second line (m')= 1/2

As m.m'=-1

Hence, the lines are perpendicular.

Ques 17)

y = -1/4x + 10 ---------(1)

-2x + 8y = 6-------(2)

On converting equation (2) we have:

As slope of first line is(m): -1/4

and that of second line is(m'): 1/4

Now,

then the lines are perpendicular.

and if m=m' then lines are parallel.

Hence, here the answer is neither.

Ques 18)

y - 4 = 5/2 (x + 3); (-7, 8)

slope of this line is: 5/2

As the line is perpendicular hence it's slope will be: -2/5

Also it passes through (-7,8) hence, the equation is:

(C). y - 8 = -2/5 (x + 7)

16

Step-by-step explanation: