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Which of the following points lie on or above the line whose equation
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27 Aug 2025, 01:19
27 Aug 2025, 01:19
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Which of the following points lie on or above the line whose equation is given by $\(12 x+16 y=8\)$ ?
Indicate all such points.
\(\boxed{A}\) $\((-2,2)\)$
\(\boxed{B}\) $\(\left(0,-\frac{1}{2}\right)\)$
\(\boxed{C}\) $\(\left(-4, \frac{9}{2}\right)\)$
\(\boxed{D}\) $\((6,-2)\)$
\(\boxed{E}\) $\((16,-12)\)$
Indicate all such points.
\(\boxed{A}\) $\((-2,2)\)$
\(\boxed{B}\) $\(\left(0,-\frac{1}{2}\right)\)$
\(\boxed{C}\) $\(\left(-4, \frac{9}{2}\right)\)$
\(\boxed{D}\) $\((6,-2)\)$
\(\boxed{E}\) $\((16,-12)\)$
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Re: Which of the following points lie on or above the line whose equation
[#permalink]
31 Aug 2025, 08:43
31 Aug 2025, 08:43
Expert Reply
The given line equation is:
$$
\(12 x+16 y=8\)
$$
To determine if a point lies on or above the line, we:
1. Substitute the $x$ and $y$ coordinates of the point into the left side of the equation $\(12 x+16 y\)$.
2. Compare $12 x+16 y$ with the constant 8 .
- If $\(12 x+16 y=8\)$, the point lies on the line.
- If $\(12 x+16 y>8\)$, the point lies above the line.
- If $\(12 x+16 y<8\)$, the point lies below the line.
Check each point:
A. \((-2, 2)\):
$$
\(12(-2)+16(2)=-24+32=8 \quad(=8) \quad \Rightarrow \text { On the line }\)
$$
B. $\\(left(0,-\frac{1}{2}\right)\)$ :
$$
\(12(0)+16\left(-\frac{1}{2}\right)=0-8=-8 \quad(<8) \quad \Rightarrow \text { Below the line }\)
$$
C. $\(\left(-4, \frac{9}{2}\right)\)$ :
$$
\(12(-4)+16\left(\frac{9}{2}\right)=-48+72=24 \quad(>8) \quad \Rightarrow \text { Above the line }\)
$$
D. $\((6,-2)\)$ :
$$
\(12(6)+16(-2)=72-32=40 \quad(>8) \quad \Rightarrow \text { Above the line }\)
$$
E. \((16, -12)\):
$$
\(12(16)+16(-12)=192-192=0 \quad(<8) \quad \Rightarrow \text { Below the line }\)
$$
Final points on or above the line:
- $\(\mathrm{A}(-2,2)-\)$ on the line
- C $\(\left(-4, \frac{9}{2}\right)\)$ - above the line
- $\(\mathrm{D}(6,-2)\)$ - above the line
Answer:
Points A, C, and D lie on or above the line.
$$
\(12 x+16 y=8\)
$$
To determine if a point lies on or above the line, we:
1. Substitute the $x$ and $y$ coordinates of the point into the left side of the equation $\(12 x+16 y\)$.
2. Compare $12 x+16 y$ with the constant 8 .
- If $\(12 x+16 y=8\)$, the point lies on the line.
- If $\(12 x+16 y>8\)$, the point lies above the line.
- If $\(12 x+16 y<8\)$, the point lies below the line.
Check each point:
A. \((-2, 2)\):
$$
\(12(-2)+16(2)=-24+32=8 \quad(=8) \quad \Rightarrow \text { On the line }\)
$$
B. $\\(left(0,-\frac{1}{2}\right)\)$ :
$$
\(12(0)+16\left(-\frac{1}{2}\right)=0-8=-8 \quad(<8) \quad \Rightarrow \text { Below the line }\)
$$
C. $\(\left(-4, \frac{9}{2}\right)\)$ :
$$
\(12(-4)+16\left(\frac{9}{2}\right)=-48+72=24 \quad(>8) \quad \Rightarrow \text { Above the line }\)
$$
D. $\((6,-2)\)$ :
$$
\(12(6)+16(-2)=72-32=40 \quad(>8) \quad \Rightarrow \text { Above the line }\)
$$
E. \((16, -12)\):
$$
\(12(16)+16(-12)=192-192=0 \quad(<8) \quad \Rightarrow \text { Below the line }\)
$$
Final points on or above the line:
- $\(\mathrm{A}(-2,2)-\)$ on the line
- C $\(\left(-4, \frac{9}{2}\right)\)$ - above the line
- $\(\mathrm{D}(6,-2)\)$ - above the line
Answer:
Points A, C, and D lie on or above the line.
gmatclubot
Re: Which of the following points lie on or above the line whose equation [#permalink]
31 Aug 2025, 08:43
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