Convert the following equation into standard form.
$y=15 x+8$
[?]x + y = []
Answer (1)
Subtract 15 x from both sides of the equation: y − 15 x = 15 x + 8 − 15 x .
Simplify the equation: − 15 x + y = 8 .
The equation is now in standard form.
The final answer is − 15 x + y = 8 .
Explanation
Understanding the Problem We are given the equation y = 15 x + 8 and we want to convert it into the standard form [?]x + y = [\] . This means we want to rearrange the equation so that the x and y terms are on the same side of the equation, and the constant term is on the other side.
Rearranging the Equation To convert the given equation to the standard form, we need to subtract 15 x from both sides of the equation: y − 15 x = 15 x + 8 − 15 x y − 15 x = 8 Now, we can rewrite the equation as: − 15 x + y = 8
Final Answer The equation is now in the standard form. The coefficient of x is − 15 and the constant term is 8 . Therefore, the equation in standard form is: − 15 x + y = 8
Examples
Understanding how to convert linear equations into standard form is crucial in various real-life applications. For instance, when planning a budget, you might have an equation representing your income and expenses. Converting this equation to standard form helps you quickly identify your fixed costs and how much you can allocate to variable expenses. Similarly, in physics, understanding linear relationships and their standard form helps in analyzing motion and forces.
