Q3. - Algebra 1

Question

Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form.

$\frac{1}{4}x-\frac{3}{4}y=-1$

Step-by-Step Solution

Answer

Yes, equation is a linear equation and the standard form is $4x-12y+4=0$.

Step 1. State the concept of standard form of linear equation.

A linear equation is any equation that can be written in the form $ax+by=0$, where a and b are real numbers and x is a variable. This form is sometimes called the standard form of a linear equation. 

 

No variable in a linear equation is raised to a power greater than 1. Linear equations are those equations that are of the first order.

 

Standard form of Linear Equation is $Ax+By+C=0$, where A, B and C are any integer. 

Step 2. Rewrite the equation in standard form.

In order to rewrite the equation $\frac{1}{4}x-\frac{3}{4}y=-1$ in standard form multiply each term of the equation by 4.

$$\begin{gathered} \frac{1}{4}x-\frac{3}{4}y=-1 \\ 4\cdot \frac{1}{4}x-4\cdot \frac{3}{4}y=-1\cdot 4 \\ 4x-12y=-4 \\ 4x-12y+4=-4+4\text{\hspace{0.17em} [\hspace{0.17em}Add\hspace{0.17em}4\hspace{0.17em}\hspace{0.17em}to\hspace{0.17em}\hspace{0.17em}both\hspace{0.17em}\hspace{0.17em}sides\hspace{0.17em}]} \\ 4x-12y+4=0 \end{gathered}$$

Step 3. State the Conclusion.

The equation is now in standard form where $A=4,B=-12\text{ and }C=4$. Since the variables in the equation has the highest exponent as 1, so the equation is linear.

 

Yes, this is a linear equation and the standard form is: $4x-12y+4=0$.