MathRevolution wrote:
In the x-y plane, there is line K, (x/a) + (y/b) = 1. What is the y-intercept of line K?
1) a = b
2) b = 5
I like this question a lot!
Target question: What is the y-intercept of line K? Given: The equation of line K is (x/a) + (y/b) = 1 This is a great candidate for
rephrasing the target question.
If we can rewrite the equation in slope y-intercept form, then this will help us identify the y-intercept of the line.
Slope y-intercept form looks like this
y = mx + q, where m is the slope of the line, and q is the y-intercept.
So, let's take the equation for line L and rewrite it in slope y-intercept form
Given: (x/a) + (y/b) = 1
Eliminate the fractions by multiplying both sides by ab to get: bx + ay = ab
Subtract bx from both sides; ay = -bx + ab
Divide both sides by a to get: y = (-b/a)x + b
So, the slope of like K will by -b/a, and
the y-intercept of line K will be b.
Since we're trying to determine the y-intercept, we can
rephrase the target question...
REPHRASED target question: What is the value of b? Now onto the statements....
Statement 1: a = b This is not enough information to determine the EXACT value of b.
Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: b = 5 PERFECT! This is exactly the information we are looking for! (we now know that 5 is the y-intercept of like K)
Since we can answer the
REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: B
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