# Unveiling The Geometric Essence of Algebra

## Question 1

The first question on using Geogebra to understand linear function is; what does a linear function represent geometrically? This question helps to lead students in thinking geometrically about algebraic frameworks. More over the question is elementary on the purpose and it could motivate students because they world know the solution.

## Question 2

Second question of the same subject is; what is the geometrical representation of a situation where a system of linear equation has; a unique solution, endlessly many solutions and lastly no solution at all? this question is among the most telling you once even though the answer could be solved easily by students who have undergone basic secondary education in mathematics. among the most common answers to this question include a point of an intersection, coincident parallel lines and lastly man coincidental parallel lines.

## Question 3

The last question is; try to outline to someone who does not know anything about algebra in this simplest way what a determinant is. this question is likely to yield various answers which are different among students. In most instances students are not expected to use geometric representation because the equation simply directs them to use simple languages.

## Question 1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output Solution For example, the rule that takes x as input and gives x2+5x+4 as output is a function. Using y to stand for the output we can represent this function with the equation y = x2+5x+4, and the graph of the equation is the graph of the function. Students are not yet expected use function notation such as f(x) = x2+5x+4.

## Question 2

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Solution For example, the rule that takes x as input and gives x2+5x+4 as output is a function. Using y to stand for the output we can represent this function with the equation y = x2+5x+4, and the graph of the equation is the graph of the function. Students are not yet expected use function notation such as f(x) = x2+5x+4.

### Question 3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line Solution Determine which of the functions listed below are linear and which are not linear and explain your reasoning. o y = -2x2 + 3
non-linear
o y = 2x
linear
o A = πr2
non-linear
o y = 0.25 + 0.5(x – 2) linear

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