College Math Placement Practice Test

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Prepare for your College Math Placement Test with our expert-crafted quiz! Practice with diverse question formats and detailed explanations to enhance your math skills and boost your confidence.

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What is the equation of a line in slope-intercept form with a slope of 2 and y-intercept of 3?

y = 2x + 3
y = 3x + 2
y = 2x - 3
y = -2x + 3

The correct answer is: y = 2x + 3

To understand why the correct answer represents the equation of a line in slope-intercept form, it's important to clarify the standard format for such an equation. The slope-intercept form of a line is given by the equation $ y = mx + b $, where $ m $ represents the slope and $ b $ denotes the y-intercept. In this case, the problem states that the slope is 2 and the y-intercept is 3. Substituting these values into the slope-intercept formula gives: 1. The slope $ m = 2 $ 2. The y-intercept $ b = 3 $ Thus, the equation becomes $ y = 2x + 3 $. This clearly indicates that for every unit increase in $ x $, the value of $ y $ increases by 2, and when $ x = 0 $, the value of $ y $ is 3. In contrast, the other options provided either have a different slope or y-intercept: - The option with a slope of 3 alters the rate of increase of $ y $ as $ x $ increases. - The option proposing a negative slope does not align with the positive slope of 2