College Math Placement Practice Test

To determine the x-intercept of the line represented by the equation \( 2x + 3y = 6 \), you need to find the value of \( x \) when \( y = 0 \). The x-intercept occurs at the point on the graph of the line where it crosses the x-axis, and this happens when the \( y \)-coordinate is zero.

Start by substituting \( y = 0 \) into the equation:

\[

2x + 3(0) = 6

\]

This simplifies to:

\[

2x = 6

\]

Next, solve for \( x \) by dividing both sides of the equation by 2:

\[

x = \frac{6}{2} = 3

\]

Thus, the x-intercept of the line is at \( x = 3 \). This corresponds to the point \( (3, 0) \) on the graph, meaning that when the line crosses the x-axis, the value of \( x \) is indeed 3, making it the correct answer.