Q10. - Algebra 1

Question

State whether each sentence is true or false. If false, replace the underlined word or number to make a true sentence.

In the linear equation $4x+3y=12$, the constant term is 12.

Step-by-Step Solution

Answer

False. The constant term is $\mathbf{-}\mathbf{12}$.

Step 1. State the equation of a straight line.

The general form of a straight line is given by, $Ax+By+C=0$, where, A and B are the coefficients of x and y respectively, C is the constant term.

Step 2. Find the general form of the given equation.

Compare the given equation with the general form of the equation of a straight line. 

Simplify,

$$\begin{gathered} 4x+3y=12 \\ 4x+3y-12=12-12 \\ 4x+3y-12=0 \end{gathered}$$

Step 3. Conclusion.

It is false because the general form of a linear equation is always in the form of $Ax+By+C=0$, where C is the constant term. Here, $-12$ is the constant term.