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The slope-intercept form is a way of writing linear equations. This form makes it easy to identify the slope and the y-intercept of a line.

The general formula is given by: \( y = mx + b \). Here, \( m \) represents the slope of the line, and \( b \) represents the y-intercept, which is where the line crosses the y-axis.

For the equation \( 3x - 9y = 7 \), we need to rewrite it in slope-intercept form to easily find the slope. This involves isolating the y variable on one side of the equation. Once we have \( y \) by itself, we can clearly see the values of \( m \) and \( b \).

Converting an equation to slope-intercept form simplifies solving problems involving the slope and graphing the line.

Linear equations represent straight lines on a graph. They are equations in which the highest power of the variable is one.

These equations are generally written in the form: \(Ax + By = C \) where \(A, B, \) and \(C \) are constants.

In the given example, \(3x - 9y = 7\), it's a standard form of a linear equation.

• We can manipulate this equation to get it into slope-intercept form, which allows us to identify the slope and y-intercept more easily.
• This process involves solving for y.

Linear equations are foundational in algebra and essential for understanding the relationship between variables.

Solving for y means to isolate y on one side of the equation, so it reads \(y = \) some expression.

Here's how you can solve for y in the given equation \(3x - 9y = 7 \):

• First, subtract \(3x \) from both sides to get \(-9y = -3x + 7 \).
• Next, divide every term by \(-9 \) to isolate y, resulting in \ y = \frac{-3x + 7}{-9} \.
• Lastly, simplify the equation to get \( y = \frac{1}{3} x - \frac{7}{9} \).

Now, the equation is in slope-intercept form, \(y = mx + b \), making it easy to identify the slope \ (m \frac{1}{3}) and the y-intercept (b = - \frac{7}{9}).
Solving for y transforms the equation into a more useful form for analyzing and graphing the line.