i) The geometric representation in one variable is a point located at -4.5 on the number line.
ii) The equation is in the form x = -4.5, which means it's a vertical line passing through the point (-4.5, y) for all y values.
The equation 2x + 9 = 0 can be represented geometrically in both one and two variables.
(i) Geometric representation in one variable:
In one variable (x), the equation can be represented as a point on a number line. The solution to the equation is the value of x for which the expression 2x + 9 equals zero. To find this value, solve for x:
2x + 9 = 0
Subtract 9 from both sides:
2x = -9
Divide by 2:
x = -4.5
So, the geometric representation in one variable is a point located at -4.5 on the number line.
(ii) Geometric representation in two variables:
In two variables (x, y), the equation 2x + 9 = 0 represents a straight line in the Cartesian coordinate system. To graph the equation, rearrange it to express y in terms of x:
2x + 9 = 0
Subtract 9 from both sides:
2x = -9
Divide by 2:
x = -4.5
Now, the equation is in the form x = -4.5, which means it's a vertical line passing through the point (-4.5, y) for all y values. The line is parallel to the y-axis.
Question
Give the geometric representations of 2x + 9 = 0 as an equation
(i) in one variable
(ii) in two variables