Q1. - Algebra 1

Question

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

$y=-4x+3$

Step-by-Step Solution

Answer

Yes, the equation is a linear equation and the standard form is $4x+y-3=0$.

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 $y=-4x+3$ in standard form add 4x to both sides as follows:

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

Step 3. State the Conclusion.

The equation is now in standard form where $A=4,B=1\text{ and }C=–3$. 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: $4x+y-3=0$.