Can someone please help me with this

y = 4x

y = -1/3 × x + 6

y = x + 1

y = 1

y = 5x

Step-by-step explanation:

the slope of a line is the factor of x in the equation representing the ratio of y/x. it stands for the number of units y changes, when x changes by another number of units.

like the factor 4 tells us that when x changes by 1, then y changes by 4.

a line parallel to another line means their slopes are identical (otherwise they could not be parallel).

the slope of a perpendicular line (cutting the other line in a 90 degree angle) is simply reversing y and x in the slope ratio. so, a slope of 4 (4/1) would simply turn into 1/4.

now the 5 tasks are easy, right ?

A y=4x-1, B y=4x + c

and because B passes through the origin = (0,0),

c is 0 (0=4×0 + c = c)

B y = 4x

A y=-3x+1, B y=-1/3 × x + c

and B passes through (12,2), 2 = -1/3 × 12 + c = -4 + c,

c = 2 + 4 = 6

B y = -1/3 × x + 6

A y = ax + c for (5,6) and (7,8), B is identical

6 = a×5 + c => c = 6 - a×5

8 = a×7 + c => 8 = a×7 + 6 - a×5 = a×2 + 6

=> a×2 = 8-6 = 2

=> a = 1, c = 6 - 1×5 = 1

=> A and B y = x + 1

A is vertical. B is perpendicular to it. perpendicular to vertical is horizontal. so, B is a flat line. which means y is a constant value (the same value for whatever value of x you want to use). so it goes flat in parallel to the x-axis through what value of y ? the point (4,1) tells us that y=1

and that is the equation for B

A 15x -3y = -6 => 3y = 15x + 6 => y = 5x + 2

B is parallel, so y = 5x + c

and B passes through (4,20), 20 = 5 × 4 + c = 20 + c,

c = 20 - 20 = 0

B y = 5x

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints

plants store their excess carbohydrate in the form of starch so that it could be used as energy source later on. the excess carbohydrate is converted into starch in the plastid i.e. chloroplast & this process occurs in the presence of sunlight. it is an insoluble polymer of glucose which gets stored in cell organelles named as amyloplasts. in some plants, starch is also stored in roots and embryos.