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Let's start by understanding the standard form of a line. A line can be represented in various ways, and one of them is the standard form. The standard form is expressed as:\[ Ax + By = C \]where:

• \( A \), \( B \), and \( C \) are constants.
• \( x \) and \( y \) are variables representing any point on the line.

This form is practical for determining intercepts and analyzing the linear equation.The key characteristics:- **Characteristics of a line in standard form:** - Both \( A \) and \( B \) can’t be zero at the same time. - Ideally, \( A \) should be a positive integer if possible.Knowing the standard form helps in transitioning to other forms like the slope-intercept or intercept form. For example, starting with \(4x - 2y = 6\), you can quickly shift to finding the intercept form or isolate one variable to reach the slope-intercept form.

The x-intercept is the point where the line crosses the x-axis. At this point, the value of \( y \) is zero because it is on the x-axis.**Steps to Find the x-intercept:** 1. Begin with the equation of the line. Here, you have \( 4x - 2y = 6 \).2. Set \( y = 0 \) to determine when the line crosses the x-axis. 3. Substitute \( y = 0 \) in the equation: \[ 4x - 2(0) = 6 \] 4. Simplify to solve for \( x \).- This simplifies to \( 4x = 6 \), and dividing by 4, gives you \( x = \frac{3}{2} \).The x-intercept is \( \frac{3}{2} \), meaning the line touches the x-axis at the point \( \left( \frac{3}{2}, 0 \right) \). Knowing the x-intercept is very useful when graphing the line.

In contrast to the x-intercept, the y-intercept is the point where the line crosses the y-axis. Here, \( x \) is zero.**Steps to Find the y-intercept:**1. Use the line’s equation, \( 4x - 2y = 6 \).2. Set \( x = 0 \) as it is the point at the y-axis.3. Insert \( x = 0 \) into the equation, resulting in: \[ 4(0) - 2y = 6 \]4. Simplify to solve for \( y \).- This results in \( -2y = 6 \). Divide by \(-2\), leading to \( y = -3 \).Thus, the y-intercept is -3, which indicates that the line intersects the y-axis at the point \((0, -3)\). This information is crucial for drafting the intercept form.