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The simplified form of \( y = \frac{2x + 2}{4} \) is \( y = \frac{x + 1}{2} \) or \( y = \frac{1}{2}x + \frac{1}{2} \).
Solution
To simplify the expression y = (2x + 2)/4, follow these steps:
1. Factor the numerator:
2x + 2 = 2(x + 1)
2. Replace the numerator in the equation:
y = [2(x + 1)] / 4
3. Cancel the common factor of 2 in the numerator and denominator:
y = (x + 1) / 2
Thus, the simplified form is:
y = (x + 1)/2 or equivalently y = ½x + ½
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Simplify this solution Mind Expander
To better understand the function \( y = \frac{2x + 2}{4} \), let’s simplify it! This expression can be reduced to \( y = \frac{1}{2}x + \frac{1}{2} \). This equation represents a straight line with a slope of \( \frac{1}{2} \), indicating that for every increase of 1 in \( x \), \( y \) increases by \( 0.5 \). Now, when you plug in values for \( x \), say \( 0 \), \( 2 \), and \( 4 \), you get \( y \) values of \( 0.5 \), \( 1.5 \), and \( 2.5 \), respectively. Plotting these points can help visualize the line and understand its upward trend. This knowledge can help you plot linear functions with ease!
