Solving Linear Equations to Isolate a Variable
This equation is a linear equation in two variables, x and y. To solve it, we want to isolate y on one side. Here's how you can do it step-by-step:
Given:
\[ y + 2 = \frac{7}{3}(x + 1) \]
Step 1: Distribute the \(\frac{7}{3}\) across the parenthesis to both x and 1.
\[ y + 2 = \frac{7}{3}x + \frac{7}{3} \]
Step 2: We want to get y on its own, so we need to subtract 2 from both sides of the equation to move the constant term on the y side to the other side.
\[ y = \frac{7}{3}x + \frac{7}{3} - 2 \]
Step 3: Combine the constant terms on the right-hand side. Since \(\frac{7}{3}\) is the same as \(2\frac{1}{3}\), you can subtract 2 from it.
\[ y = \frac{7}{3}x + \frac{1}{3} \]
Now y is expressed in terms of x. The equation here represents a line with a slope of \(\frac{7}{3}\) and a y-intercept at \(\frac{1}{3}\).
