Which equation is in standard form?
a. [tex]$x+3=-5y$[/tex]
b. [tex]$5-x=0$[/tex]
c. [tex]$y=3x+6$[/tex]
d. [tex]$-8x+3y=12$[/tex]
Answer (2)
Assume 'starelaref' is a typo for 'standard form' of a linear equation.
Recall the standard form: A x + B y = C .
Analyze each option and rewrite them in standard form if necessary.
Identify the equation that is already in standard form: − 8 x + 3 y = 12 .
Explanation
Understanding the Problem The question asks us to identify which of the given equations is in 'starelaref' term. However, 'starelaref' is not a standard mathematical term. It is likely a typo and might refer to 'standard form'. Let's assume that 'starelaref' is a typo and the question is asking which equation is in standard form.
Defining Standard Form The standard form of a linear equation is given by A x + B y = C , where A , B , and C are constants. We need to rewrite each equation in this form to determine which one fits the standard form.
Analyzing Each Option Let's analyze each option: a. x + 3 = − 5 y can be rewritten as x + 5 y = − 3 . This fits the standard form A x + B y = C , where A = 1 , B = 5 , and C = − 3 .
b. 5 − x = 0 can be rewritten as − x = − 5 or − x + 0 y = − 5 . This also fits the standard form A x + B y = C , where A = − 1 , B = 0 , and C = − 5 .
c. y = 3 r + 6 can be rewritten as 0 x − 3 r + y = 6 or 0 x + y − 3 r = 6 . This equation involves three variables, x , y , and r . If we consider only x and y , it's not in standard form. However, if we consider r as a variable, it can be written as 0 x + y − 3 r = 6 , which is a linear equation in three variables. d. − 8 x + 3 y = 12 is already in the standard form A x + B y = C , where A = − 8 , B = 3 , and C = 12 .
Determining the Correct Answer Since options a, b, and d can be written in the standard form A x + B y = C with two variables x and y , and option c involves three variables, and given the multiple-choice format, we need to select only one answer. Assuming the question is about the standard form of a linear equation in two variables ( x and y ), and without further clarification, options a, b, and d are all valid. However, since the question is likely expecting only one correct answer, and option d is already presented in the standard form without any rearrangement, it is the most straightforward answer.
Final Answer and Conclusion Therefore, the equation that is already in standard form is − 8 x + 3 y = 12 .
Examples
Understanding the standard form of linear equations is crucial in various fields, such as economics and physics. For instance, in economics, a budget constraint can be represented in standard form, where x and y represent the quantities of two goods, and the equation shows the combinations of goods that a consumer can afford. Similarly, in physics, equations representing forces or motion can be expressed in standard form to analyze the relationships between variables more easily. Knowing how to convert equations into standard form allows for easier comparison and analysis of different linear relationships.
The equation that is in standard form is − 8 x + 3 y = 12 . Options a and b can also be rearranged to standard form, but option d is already in the correct format. Therefore, the chosen answer is option d.
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