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 (−11,3)
left parenthesis negative 12 comma 2 right parenthesis and left parenthesis negative 11 comma 3 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 (−9,3)

Answer 1

To determine which set of points lies on the line represented by the equation \( y + 2 = 13(x - 12) \), let's first rewrite the equation in slope-intercept form \( y = mx + b \).

Starting with the original equation:

\[
y + 2 = 13(x - 12)
\]

Distributing \( 13 \):

\[
y + 2 = 13x - 156
\]

Subtracting \( 2 \) from both sides:

\[
y = 13x - 158
\]

Now, we need to check each set of points to see if they satisfy this equation.

### Set (12, -2) and (15, -1)
1. For \( (12, -2) \):
\[
y = 13(12) - 158 = 156 - 158 = -2 \quad \text{(True)}
\]
2. For \( (15, -1) \):
\[
y = 13(15) - 158 = 195 - 158 = 37 \quad \text{(False)}
\]

### Set (−12, 2) and (−11, 3)
1. For \( (-12, 2) \):
\[
y = 13(-12) - 158 = -156 - 158 = -314 \quad \text{(False)}
\]
2. For \( (-11, 3) \):
\[
y = 13(-11) - 158 = -143 - 158 = -301 \quad \text{(False)}
\]

### Set (12, -2) and (13, 1)
1. For \( (12, -2) \):
\[
y = 13(12) - 158 = -2 \quad \text{(True)}
\]
2. For \( (13, 1) \):
\[
y = 13(13) - 158 = 169 - 158 = 11 \quad \text{(False)}
\]

### Set (−12, 2) and (−9, 3)
1. For \( (-12, 2) \):
\[
y = 13(-12) - 158 = -314 \quad \text{(False)}
\]
2. For \( (-9, 3) \):
\[
y = 13(-9) - 158 = -117 - 158 = -275 \quad \text{(False)}
\]

Based on the calculations, none of the point sets have both points lying on the line.

However, since \( (12, -2) \) is the only point that satisfies the equation from the first set, the answer is:

**Set (12, -2) which is present in the first and third options** is one point that lies on the line.