College Math Placement Practice Test

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What is the x-intercept of the line given by the equation 2x + 3y = 6?

x-intercept = 1
x-intercept = 2
x-intercept = 3
x-intercept = 4

The correct answer is: x-intercept = 3

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.