Write the linear equation $4y = 7x - 10$ in standard form.
Answer (1)
Rearrange the given equation 4 y = 7 x − 10 .
Subtract 7 x from both sides: − 7 x + 4 y = − 10 .
The equation is now in standard form: − 7 x + 4 y = − 10 .
Alternatively, multiply by -1: 7 x − 4 y = 10 . The final answer is − 7 x + 4 y = − 10 .
Explanation
Understanding the Problem We are given the equation 4 y = 7 x − 10 and asked to write it in standard form. The standard form of a linear equation is A x + B y = C , where A , B , and C are constants.
Rearranging the Equation To convert the given equation to standard form, we need to move the 7 x term to the left side of the equation. We can do this by subtracting 7 x from both sides: 4 y − 7 x = 7 x − 10 − 7 x 4 y − 7 x = − 10
Writing in Standard Form Now, we can rearrange the terms on the left side to match the standard form A x + B y = C :
− 7 x + 4 y = − 10
Final Answer So, the equation in standard form is − 7 x + 4 y = − 10 . Alternatively, we can multiply the entire equation by -1 to get 7 x − 4 y = 10 . Both forms are acceptable.
Examples
Linear equations in standard form are useful in various real-life scenarios. For example, if you are buying two types of items, like apples and bananas, and you have a fixed budget, you can represent the relationship between the quantities of apples and bananas you can buy with a linear equation in standard form. This helps you determine the different combinations of apples and bananas you can afford within your budget, making it easier to plan your purchases.
