Question

If a line can be represented by the equation y+2=13(x−12) , which of the following sets of points lies on the line?(1 point)
Responses

(12,−2) and (15,−1)
left parenthesis 12 comma negative 2 right parenthesis and left parenthesis 15 comma negative 1 right parenthesis

(12,−2) and (13,1)
left parenthesis 12 comma negative 2 right parenthesis and left parenthesis 13 comma 1 right parenthesis

(−12,2) and (−11,3)
left parenthesis negative 12 comma 2 right parenthesis and left parenthesis negative 11 comma 3 right parenthesis

(−12,2) and (−9,3)

Answer 1

To determine which of the given points lies on the line represented by the equation \( y + 2 = 13(x - 12) \), we first rearrange the equation into slope-intercept form ( \( y = mx + b \) ) as follows:

1. Subtract 2 from both sides:
\[
y = 13(x - 12) - 2
\]
2. Distribute the 13:
\[
y = 13x - 156 - 2
\]
3. Simplify:
\[
y = 13x - 158
\]

Now, let's test each pair of points to see if they satisfy the line equation \( y = 13x - 158 \).

1. **Testing (12, -2) and (15, -1)**:
- For (12, -2):
\[
-2 = 13(12) - 158 \implies -2 = 156 - 158 \implies -2 = -2\quad (True)
\]
- For (15, -1):
\[
-1 = 13(15) - 158 \implies -1 = 195 - 158 \implies -1 = 37\quad (False)
\]

2. **Testing (12, -2) and (13, 1)**:
- For (12, -2):
\[
-2 = 13(12) - 158 \implies -2 = 156 - 158 \implies -2 = -2\quad (True)
\]
- For (13, 1):
\[
1 = 13(13) - 158 \implies 1 = 169 - 158 \implies 1 = 11\quad (False)
\]

3. **Testing (−12, 2) and (−11, 3)**:
- For (−12, 2):
\[
2 = 13(-12) - 158 \implies 2 = -156 - 158 \implies 2 = -314\quad (False)
\]
- For (−11, 3):
\[
3 = 13(-11) - 158 \implies 3 = -143 - 158 \implies 3 = -301\quad (False)
\]

4. **Testing (−12, 2) and (−9, 3)**:
- For (−12, 2):
\[
2 = 13(-12) - 158 \implies 2 = -156 - 158 \implies 2 = -314\quad (False)
\]
- For (−9, 3):
\[
3 = 13(-9) - 158 \implies 3 = -117 - 158 \implies 3 = -275\quad (False)
\]

After checking each set of points, we find that the only point that fits is (12, -2) but it is not in a valid pairing from the options given. However, none of the pairs contain two points that are both on the line. Thus, none of the options listed are fully correct.

Therefore, the answer is that none of the sets of points provided lie on the line.