Line k lies in the xy-plane. The x-intercept of line k is ?4, and line k passes through the midpoint of the line segment whose endpoints are and (2, 9) and (2, 0). What is the slope of line k? Give your answer as a fraction.
Excellent question! In this problem, we're asked for the slope of line k as a fraction. While our initial answer of 4.5/6 is a fraction, there is a decimal in the numerator. Based on general math conventions, though, we want to avoid decimals in fractions. We can easily get rid of the decimal in the numerator by multiplying the fraction by 2/2. When we do so, we get 9/12. We haven't changed the overall value of the fraction, since 2/2 = 1. However, in this new form, we do have a fraction with integers in both the numerator and denominator! From here, we could reduce this fraction to 9/12 = 3/4. However, on the GRE, you do not have to write a fraction in its most reduced form. So, for a numeric entry question, you could input 9/12 or 3/4, and still be correct :)
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