into standard form.
$y=-3 x-10$
[?] x+y=
Answer (1)
Add 3 x to both sides of the equation.
Simplify the equation to get 3 x + y = − 10 .
The equation is now in standard form.
The final answer is 3 x + y = − 10 .
Explanation
Understanding the Problem We are given the equation y = − 3 x − 10 and we want to convert it into the standard form A x + y = C . This means we need to move the term with x to the left side of the equation.
Isolating the Constant Term To convert the equation to the standard form, we add 3 x to both sides of the equation: y + 3 x = − 3 x − 10 + 3 x 3 x + y = − 10
Final Answer The equation is now in the standard form A x + y = C , where A = 3 and C = − 10 . Therefore, the equation in standard form is 3 x + y = − 10 .
Examples
Understanding standard form equations is crucial in various fields, such as physics and engineering, where linear relationships are frequently encountered. For instance, in circuit analysis, the voltage-current relationship in a resistor can be expressed in standard form, aiding in the calculation of circuit parameters. Similarly, in economics, linear cost functions can be represented in standard form to analyze production costs and make informed business decisions. Mastering the transformation of equations into standard form enhances problem-solving skills and provides a solid foundation for more advanced mathematical concepts.
