Which of the following statements is correct?a)An equation of first degree always represents a straight lineb)An equation of first degree may or may not represent a straight linec)Every equation of odd degree always represents a straight lined)Only an equation of the type x/a + y/b = 1 represents a straight line, where a and b are the intercepts made by the straight line on x-axis and y-axis respectivelyCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

An equation of first degree always represents a straight line. This is because an equation of first degree can be written in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.

Explanation:
Let's break down the statement and understand each part:

Equation of first degree: An equation of first degree is a polynomial equation where the highest power of the variable is 1. It can be written as ax + by + c = 0, where a, b, and c are constants, and x and y are variables.

Represents a straight line: When an equation of first degree is written in the form y = mx + b, it represents a straight line on the coordinate plane. The variable y represents the dependent variable, x represents the independent variable, m represents the slope of the line, and b represents the y-intercept (the point where the line intersects the y-axis).

Proof:

1. Slope-intercept form: An equation of first degree can always be rearranged into the slope-intercept form y = mx + b. This form directly represents a straight line, where m is the slope and b is the y-intercept.

2. Constant slope: In the equation y = mx + b, the coefficient of x, which is m, represents the slope of the line. Since the slope is constant, the line will always be a straight line.

3. Linear relationship: Equations of first degree represent a linear relationship between the variables x and y. This means that for every unit increase in x, there will be a corresponding change in y that can be represented by the slope m. This linear relationship is characteristic of a straight line.

4. Graphical representation: When we plot the points that satisfy the equation of first degree on a coordinate plane, we always obtain a straight line. This can be proven by selecting a few values of x, calculating the corresponding values of y using the equation, and then plotting these points. The resulting graph will always be a straight line.

Therefore, based on the above explanations and proofs, it can be concluded that an equation of first degree always represents a straight line.

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