Exercise 6.5

Give the graphical representation of the equation.

x = 3

Solution:

(a) On the number line

On a number line, the equation x = 3 represents a single point at the value .

On the Cartesian plane

On the Cartesian plane, the equation x = represents a vertical line passing through the point (, ) on the x-axis.

(ii) y + 3 = 0

Solution:

(a) On the number line

On a number line, the equation y + 3 = 0 represents a single point at the value .

On the Cartesian plane

On the Cartesian plane, the equation y = represents a vertical line passing through the point (, ) on the x-axis.

(iii) y = 4

Solution:

(a) On the number line

On a number line, the equation y = 4 represents a single point at the value .

On the Cartesian plane

On the Cartesian plane, the equation x = represents a vertical line passing through the point (40, 04) on the x-axis.

Give the graphical representation of the equation.

(iv) 2x – 9 = 0

Solution:

(a) On the number line

To find the value of x, we need to isolate x in the equation:

2x – 9 = 0

=> 2x = 9

Divide both sides by 2:

=> x = 9229 =

On the Cartesian plane

On the Cartesian plane, the equation x = represents a vertical line passing through the point (4.50, 04.5) on the x-axis.

Give the graphical representation of the equation.

(v) 3x + 5 = 0

Solution:

(a) On the number line

First, solve for x: 3x + 5 = 0

=> 3x = -55

=> x = −5353 ≈ -1.671.57.

On a number line, this represents a single point at -1.67

On the Cartesian plane

On the Cartesian plane, the equation 3x + 5 = 0 represents a vertical line passing through the point (-1.670, 01.67) on the x-axis.

2. Give the graphical representation of 2x - 11 = 0 as an equation in one variable

Solution:

Solving for x, we get:

2x - 11 = 0

2x = 11-11

x = 112−112 =

This represents a single point on the number line at the value 5.5.

On the Cartesian plane

On the Cartesian plane, the equation 2x - 11 = 0 represents a vertical line passing through the point (5.50, 05.5) on the x-axis.

3. Solve the equation 3x + 2 = 8x - 8 and represent the solution on

(i) the number line (ii) the Cartesian plane

Solution:

Solving the equation:

Given 3x + 2 = 8x - 8

=> 2 + 8 = 8x -

=> =

=> x = 105510

=> x =

(i) On the number line:

The solution x = 2 is represented as a single point on the number line.

On the Cartesian plane

On the Cartesian plane, the equation 3x + 2 = 8x - 8 represents a verticalhorizontal line passing through the point ( , ) on the x-axis.

Write the equation of the line parallel to the X-axis and passing through the point

(i) (0 , -3)

Solution:

A line parallel to the x-axis will have a constantvariabley-value. Therefore, the equation of the line will be of the form y = k, where k is a constant.

The line passes through (0, -3), so the equation is y = .

(ii) (0, 4)

Solution:

The line passes through (0 , 4), so the equation is y = .

(iii) (2, -5)

Solution:

The line passes through (2 , -5), so the equation is y = .

(iv) (3, 4)

Solution:

The line passes through (3 , 4), so the equation is y = .

5. Write the equation of the line parallel to the Y-axis and passing through the point

(i) (-4, 0)

Solution:

A line parallel to the y-axis will have a constantvariable x-value. Therefore, the equation of the line will be of the form x = k, where k is a constant.

The line passes through (-4, 0), so the equation is x = .

(ii) (2, 0)

Solution:

The line passes through (2, 0), so the equation is x = .

(iii) (3, 5)

Solution:

The line passes through (3, 5), so the equation is x = .

(iv) (-4, -3)

Solution:

The line passes through (-4, -3), so the equation is x = .

Write the equation of three lines that are

(i) parallel to the X-axis

Solution:

Lines parallel to the x-axis have the equation y = kx, where k is a constantvariable. So, three examples would be:

y = 2

y = -5

y = 0

(ii) parallel to the Y-axis

Solution:

Lines parallel to the y-axis have the equation x = ky, where k is a constantvariable. So, three examples would be:

x = 1

x = -3

x = 7