Questions: Determining whether given points lie on one, both, or neither of 2 lines... For each point in the table below, decide whether it is on Line 1, Line 2, both, or neither. Line 1: -9x+11y=-8 Line 2: -4x+9y=17 (x, y) Line 1 Line 2 Both Lines Neither Line (-2,1) 0 0 0 0 (4,-6) 0 0 0 0 (-4,-4) 0 0 0 0

Determining whether given points lie on one, both, or neither of 2 lines...

For each point in the table below, decide whether it is on Line 1, Line 2, both, or neither.
Line 1: -9x+11y=-8
Line 2: -4x+9y=17

(x, y)  Line 1  Line 2  Both Lines  Neither Line
(-2,1)  0  0  0  0
(4,-6)  0  0  0  0
(-4,-4)  0  0  0  0
Transcript text: Determining whether given points lie on one, both, or neither of 2 lines... For each point in the table below, decide whether it is on Line 1, Line 2, both, or neither. Line 1: $-9 x+11 y=-8$ Line 2: $-4 x+9 y=17$ \begin{tabular}{|c|c|c|c|c|} \hline$(x, y)$ & Line 1 & Line 2 & \begin{tabular}{c} Both \\ Lines \end{tabular} & \begin{tabular}{c} Neither \\ Line \end{tabular} \\ \hline$(-2,1)$ & 0 & 0 & 0 & 0 \\ \hline$(4,-6)$ & 0 & 0 & 0 & 0 \\ \hline$(-4,-4)$ & 0 & 0 & 0 & 0 \\ \hline \end{tabular}
failed

Solution

failed
failed

Determine whether the point \((-2, 1)\) lies on Line 1, Line 2, both, or neither.

Check if \((-2, 1)\) lies on Line 1: \(-9x + 11y = -8\).

Substitute \(x = -2\) and \(y = 1\) into Line 1:
\[ -9(-2) + 11(1) = 18 + 11 = 29 \neq -8.
\]
The point \((-2, 1)\) does not lie on Line 1.

Check if \((-2, 1)\) lies on Line 2: \(-4x + 9y = 17\).

Substitute \(x = -2\) and \(y = 1\) into Line 2:
\[ -4(-2) + 9(1) = 8 + 9 = 17.
\]
The point \((-2, 1)\) lies on Line 2.

The point \((-2, 1)\) lies on Line 2 only.
\(\boxed{\text{Line 2}}\)

Determine whether the point \((4, -6)\) lies on Line 1, Line 2, both, or neither.

Check if \((4, -6)\) lies on Line 1: \(-9x + 11y = -8\).

Substitute \(x = 4\) and \(y = -6\) into Line 1:
\[ -9(4) + 11(-6) = -36 - 66 = -102 \neq -8.
\]
The point \((4, -6)\) does not lie on Line 1.

Check if \((4, -6)\) lies on Line 2: \(-4x + 9y = 17\).

Substitute \(x = 4\) and \(y = -6\) into Line 2:
\[ -4(4) + 9(-6) = -16 - 54 = -70 \neq 17.
\]
The point \((4, -6)\) does not lie on Line 2.

The point \((4, -6)\) lies on neither line.
\(\boxed{\text{Neither Line}}\)

Determine whether the point \((-4, -4)\) lies on Line 1, Line 2, both, or neither.

Check if \((-4, -4)\) lies on Line 1: \(-9x + 11y = -8\).

Substitute \(x = -4\) and \(y = -4\) into Line 1:
\[ -9(-4) + 11(-4) = 36 - 44 = -8.
\]
The point \((-4, -4)\) lies on Line 1.

Check if \((-4, -4)\) lies on Line 2: \(-4x + 9y = 17\).

Substitute \(x = -4\) and \(y = -4\) into Line 2:
\[ -4(-4) + 9(-4) = 16 - 36 = -20 \neq 17.
\]
The point \((-4, -4)\) does not lie on Line 2.

The point \((-4, -4)\) lies on Line 1 only.
\(\boxed{\text{Line 1}}\)

The point \((-2, 1)\) lies on Line 2 only.
The point \((4, -6)\) lies on neither line.
The point \((-4, -4)\) lies on Line 1 only.

Was this solution helpful?
failed
Unhelpful
failed
Helpful