Q60. - Algebra 2

Question

Write each equation in standard form. Identify A, B, and C.

$60. y=7x+4$

Step-by-Step Solution

Answer

The standard form of the equation is $-7x+y=4$ and $A=-7, B=1, C=4$.

Step-1 – Apply the concept of Standard form of equation

Any linear equation with variables x and y can be expressed in the standard form as:

$Ax+By=C$

Where A, B, and C are all integers with greatest common factor as 1.

Step-2 – Convert the equation into standard form

Consider the given equation.

$y=7x+4$

To convert it into standard form, subtract $-7x$ on both sides of equation.

$\begin{array}{c}y-7x=7x+4-7x\\ -7x+y=4\end{array}$

Thus, the standard form of the equation is $-7x+y=4$.

Step-3 – Identification of A, B, and C

Comparing $-7x+y=4$ with standard form $Ax+By=C$, we get

$\begin{array}{l}A=-7\\ B=1\\ C=4\end{array}$

Hence, the standard form of the equation is $-7x+y=4$ and $A=-7, B=1, C=4$.