In the \(xy-\)plane, line \(a\) and line \(b\) have the same

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In the \(xy-\)plane, line \(a\) and line \(b\) have the same slope. If the \(y-\)intercept of line \(a\) is -1, what is the \(y-\)intercept of line \(b\)?

1) The \(x-\)intercept of line \(a\) is -1.
2) Line \(b\) passes through the point \((10, 20)\).

The OA is C

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by Ian Stewart » Wed Aug 14, 2019 6:54 am

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Using only Statement 1, we know two different points on line a (the x-intercept and the y-intercept), so we can find the slope of line a. Since lines a and b have the same slope, we can therefore find the slope of line b. But we have no idea where line b is, so we can't find its y-intercept.

Using only Statement 2, we know only one point on line b, and it's not the point we're asked to find (the y-intercept). The y-intercept of line b could be anything, depending on the slope of the line.

Using both Statements, we know the slope of line b from Statement 1, and a point on line b from Statement 2, so we know exactly what line b is, and can answer any question about it, so the answer is C.
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