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In the XY-plane, lines a and b are parallel. If both the X- intercept
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19 Jan 2024, 06:22
19 Jan 2024, 06:22
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In the XY-plane, lines a and b are parallel. If both the X- intercept and the Y-intercept of line a is −1, and line b passes through the point (10, 20), what is the Y-intercept of line b?
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30
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In the XY-plane, lines a and b are parallel. If both the X- intercept
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19 Jan 2024, 21:02
19 Jan 2024, 21:02
1
The x-intercept is the point where the line crosses the x-axis, i.e., when y = 0. Therefore, (-1, 0) is a point on line a.
Likewise, y = -1 when x = 0, so (0, -1) is also a point on line a.
Now that we have 2 points on line a, we can find its slope:
\(\frac{y2-y1}{x2-x1} = \frac{-1-0}{0-(-1)} = -1\)
Since lines a and b are parallel, they have the same slope. We can plug in the given point (10, 20) into the equation y = mx+b:
\(20 = (-1)(10) + b\)
\(b = 30\)
Likewise, y = -1 when x = 0, so (0, -1) is also a point on line a.
Now that we have 2 points on line a, we can find its slope:
\(\frac{y2-y1}{x2-x1} = \frac{-1-0}{0-(-1)} = -1\)
Since lines a and b are parallel, they have the same slope. We can plug in the given point (10, 20) into the equation y = mx+b:
\(20 = (-1)(10) + b\)
\(b = 30\)
gmatclubot
In the XY-plane, lines a and b are parallel. If both the X- intercept [#permalink]
19 Jan 2024, 21:02
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