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In the x y-coordinate system, line k passes
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03 Jun 2026, 08:43
03 Jun 2026, 08:43
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Question Stats:
93% (01:37) correct
6% (01:38) wrong based on 15 sessions
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In the x y-coordinate system, line k passes through points \((-5 \mathrm{~m}, 0)\) and \((0,2 \mathrm{~m})\). Which of the following is a possible equation of line k ?
\(\begin{aligned}
& A. y=-\frac{5}{2} x+2 m \\
& B. y=\frac{2}{5} x-5 m \\
& C. y=\frac{5}{2} x+2 m \\
& D. y=\frac{2}{5} x+2 m \\
& E. y=-\frac{2}{5} x-5 m
\end{aligned}\)
\(\begin{aligned}
& A. y=-\frac{5}{2} x+2 m \\
& B. y=\frac{2}{5} x-5 m \\
& C. y=\frac{5}{2} x+2 m \\
& D. y=\frac{2}{5} x+2 m \\
& E. y=-\frac{2}{5} x-5 m
\end{aligned}\)
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Re: In the x y-coordinate system, line k passes
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05 Jun 2026, 10:45
05 Jun 2026, 10:45
Expert Reply
Explanation
The missing points are \((-5m, 0)\) and \((0, 2m),\).
Find the slope of line \(k\)
The slope formula for a line passing through two points (x1, y1) and (x2, y2) is:
Slope = \(\frac{y2-y1}{x2-x1}\)
Substituting the points \((-5m, 0)\) and \((0, 2m):\)
Slop = \(\frac{2m-0}{0-(-5m)} = \frac{2m}{5m}=\frac{2}{5}\)
Since m cancels out, the slope of line k must be exactly \(\frac{2}{5}\). Looking at the answer choices, we can immediately eliminate A, C, and E, leaving only B and D as possibilities because they have a slope of \(\frac{2}{5}\)
The point \((0, 2m)\) explicitly represents the y-intercept of the line because its x-coordinate is 0. Using the slope-intercept form \((y = sx + b)\), where s = \(\frac{2}{5}\) and the y-intercept \(b = 2m:\)
\(y = (\frac{2}{5})x + 2m\)
Answer: D
The missing points are \((-5m, 0)\) and \((0, 2m),\).
Find the slope of line \(k\)
The slope formula for a line passing through two points (x1, y1) and (x2, y2) is:
Slope = \(\frac{y2-y1}{x2-x1}\)
Substituting the points \((-5m, 0)\) and \((0, 2m):\)
Slop = \(\frac{2m-0}{0-(-5m)} = \frac{2m}{5m}=\frac{2}{5}\)
Since m cancels out, the slope of line k must be exactly \(\frac{2}{5}\). Looking at the answer choices, we can immediately eliminate A, C, and E, leaving only B and D as possibilities because they have a slope of \(\frac{2}{5}\)
The point \((0, 2m)\) explicitly represents the y-intercept of the line because its x-coordinate is 0. Using the slope-intercept form \((y = sx + b)\), where s = \(\frac{2}{5}\) and the y-intercept \(b = 2m:\)
\(y = (\frac{2}{5})x + 2m\)
Answer: D
gmatclubot
Re: In the x y-coordinate system, line k passes [#permalink]
05 Jun 2026, 10:45
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