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\( 4 x+2 y=8 \quad \) Function

Ask by Rojas Ortega. in the United States
Feb 19,2025

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The function is \( f(x) = 4 - 2x \).

Solución

We start with the equation: 4x + 2y = 8. To write it as a function (in slope-intercept form), solve for y as follows: 1. Subtract 4x from both sides:   2y = 8 - 4x 2. Divide the entire equation by 2:   y = 4 - 2x Thus, the function form is:   f(x) = 4 - 2x

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Bonus Knowledge

Did you know that the equation \( 4x + 2y = 8 \) can be rewritten in slope-intercept form, which is \( y = mx + b \)? If you do a little rearranging, you can find that the equation simplifies to \( y = -2x + 4 \). This shows that the slope (\(m\)) is -2, meaning that for every increase of 1 unit in \(x\), \(y\) will decrease by 2 units! In the real world, linear equations like this one are used to model relationships between variables. For instance, imagine you're tracking your savings over time. If you start with $8 and save $2 less for every day you track (maybe you’re spending some), this formula could represent your savings over time. It's a simple yet powerful way to visualize how things change!

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