Question

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

$y=-4x+3$

Short answer

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

Step-by-step solution

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

Alinear equationis anyequationthat 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 alinear equationis raised to a power greater than 1. Linear equationsare 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:$4x+y-3=0$.