2. Coordination in Plants

Basics Revisited

Equation

An equation is a statement that two mathematical expressions having one or more variables are equal.

Linear Equation

Equations in which the powers of all the variables involved are one are called linear equations. The degree of a linear equation is always one.

General form of a Linear Equation in Two Variables

The general form of a linear equation in two variables is ax + by + c = 0, where a and b cannot be zero simultaneously.

Representing linear equations for a word problem

To represent a word problem as a linear equation

• Identify unknown quantities and denote them by variables.
• Represent the relationships between quantities in a mathematical form, replacing the unknowns with variables.

Solution of a Linear Equation in 2 variables

The solution of a linear equation in two variables is a pair of values, one for x and the other for y, which makes the two sides of the equation equal.
Eg: If 2x+y=4, then (0,4) is one of its solutions as it satisfies the equation. A linear equation in two variables has infinitely many solutions.

Geometrical Representation of a Linear Equation

Geometrically, a linear equation in two variables can be represented as a straight line.
2x – y + 1 = 0

⇒ y = 2x + 1

Graph of y = 2

x

+1

Plotting a Straight Line

The graph of a linear equation in two variables is a straight line. We plot the straight line as follows:

Any additional points plotted in this manner will lie on the same line.

All about Lines

General form of a pair of linear equations in 2 variables

A pair of linear equations in two variables can be represented as follows
 

The coefficients of x and y cannot be zero simultaneously for an equation.

Nature of 2 straight lines in a plane

For a pair of straight lines on a plane, there are three possibilities

i) They intersect at exactly one point

pair of linear equations which intersect at a single point.

ii) They are parallel

pair of linear equations which are parallel.

iii) They are coincident

pair of linear equations which are coincident.

Graphical Solution

Representing pair of LE in 2 variables graphically

Graphically, a pair of linear equations in two variables can be represented by a pair of straight lines.

Graphical method of finding solution of a pair of Linear Equations

Graphical Method  of finding the solution to a pair of linear equations is as follows:

• Plot both the equations (two straight lines)
• Find the point of intersection of the lines.

The point of intersection is the solution.

Comparing the ratios of coefficients of a Linear Equation

Algebraic Solution

Finding solution for consistent pair of Linear Equations

The solution of a pair of linear equations is of the form (x,y) which satisfies both the equations simultaneously. Solution for a consistent pair of linear equations can be found out using

i) Elimination method

ii) Substitution Method

iii) Cross-multiplication method

iv) Graphical method

Substitution Method of finding solution of a pair of Linear Equations

Substitution method:

y – 2x = 1

x + 2y = 12

(i) express one variable in terms of the other using one of the equations. In this case, y = 2x + 1.

(ii) substitute for this variable (y) in the second equation to get a linear equation in one variable, x. x + 2 × (2x + 1) = 12

⇒ 5 x + 2 = 12

(iii) Solve the linear equation in one variable to find the value of that variable.
5 x + 2 = 12
⇒ x = 2

(iv) Substitute this value in one of the equations to get the value of the other variable.

y = 2 × 2 + 1

⇒y = 5

So, (2,5) is the required solution of the pair of linear equations y – 2x = 1 and x + 2y = 12.

Elimination method of finding solution of a pair of Linear Equations

Elimination method
Consider x + 2y = 8 and 2x – 3y = 2

Step 1: Make the coefficients of any variable the same by multiplying the equations with constants. Multiplying the first equation by 2, we get,

2x + 4y = 16

Step 2: Add or subtract the equations to eliminate one variable, giving a single variable equation.
Subtract second equation from the previous equation
2x + 4y = 16
2x  – 3y =  2
–     +       –
———————–
0(x) + 7y =14
Step 3: Solve for one variable and substitute this in any equation to get the other variable.

y = 2,

x = 8 – 2 y

⇒ x = 8 – 4

⇒ x = 4

(4, 2) is the solution.

Coordination in plants

Plants though do not have nervous system or muscles but they also respond towards the stimulus. For example, when we touch Mimosa pudica (touch-me-not plant), its leaves fold up and droop. There are two types of movements in plants -dependent on growth and independent of growth. When we touch the Mimosa pudica, its leaves fold up but no growth occurs, so it does not involve any growth. But movement of seedling is due to growth. Plants convey information from cell to cell through electrical-chemical means.

Hormone produced by plants

Movement due to Growth

The most common example of movement of growth are tendrils. Tendrils are sensitive to touch. When they come in contact with some object, the part of tendril away from the object will grow fast compare to the part of tendril which is in contact with the object. So it is a directional movement and it appears as if the plant is moving.
Directional movements of the plants are known as tropic movements. The movement can be towards the stimulus or away from the stimulus. Examples of some movements in plants are mentioned below-

 Many plant hormones are responsible for various kinds of movements in plants. Movements in plants can be divided into two main types:

1. Tropic movement
2. Nastic movement

1. Tropic Movement: The movements which are in a particular direction in relation to the stimulus are called tropic movements. Tropic movements happen as a result of growth of a plant part in a particular direction. There are four types of tropic movements.

(i) Geotropic movement: The growth in a plant part in response to the gravity is called geotropic movement. Roots usually show positive geotropic movement, i.e. they grow in the direction of the gravity. Stems usually show negative geotropic movement.
(ii) Phototropic Movement: The growth in a plant part in response to light is called phototropic movement. Stems usually show positive phototropic movement, while roots usually show negative phototropic movement. If a plant is kept in a container in which no sunlight reaches and a hole in the container allows some sunlight; the stem finally grows in the direction of the sunlight. This happens because of a higher rate of cell division in the part of stem which is away from the sunlight. As a result, the stem bends towards the light. The heightened rate of cell division is attained by increased secretion of the plant hormone auxin in the is away from sunlight.
(iii) Hydrotropic Movement: When roots grow in the soil, they usually grow towards the nearest source of water. This shows a positive hydrotropic movement.
(iv) Thigmotropism Movement: The growth in a plant part in response to touch is called thigmotropism movement. Such movements are seen in tendrils of climbers. The tendril grows in a way so as it can coil around a support. The differential rate of cell division in different parts of the tendril happens due to action of auxin. 

2. Nastic Movement: The movement which do not depend on the direction from the stimulus acts are called nastic movement. For example, when someone touches the leaves of mimosa, the leaves droop. The drooping is independent of the direction from which the leaves are touched. Such movements usually happen because of changing water balance in the cells. When leaves of mimosa are touched, the cells in the leaves lose- water and become flaccid, resulting in drooping of leaves.