The equation you provided is a linear equation in two variables: \(x\) and \(y\).

To express one variable in terms of the other, let's solve for \(y\) in terms of \(x\):

\[
6x + 2y = 10
\]

1. Subtract \(6x\) from both sides:
\[
2y = 10 - 6x
\]

2. Divide both sides by 2:
\[
y = \frac{10 - 6x}{2}
\]

Simplify:
\[
y = 5 - 3x
\]

So, the equation in terms of \(y\) is \(y = 5 - 3x\). This is the slope-intercept form, where the slope is \(-3\) and the y-intercept is \(5\).

Do you want more details or have any questions?

Here are 5 related questions:
1. How do you find the slope of a line from an equation?
2. How can we graph this line on a coordinate plane?
3. Can we solve this system of equations with another linear equation?
4. What is the interpretation of the y-intercept in real-life problems?
5. How can we find the x-intercept from the equation?

**Tip:** To find the x-intercept, set \(y = 0\) in the equation and solve for \(x\).

Learn how to solve the linear equation 6x + 2y = 10 and express it in slope-intercept form. This step-by-step solution explains key algebraic concepts, including finding the slope and y-intercept. Suitable for students in Grades 7-10.

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