To determine which of the given coordinates lies on the line described by the equation [tex]\( y = 2x + 4 \)[/tex], we need to check each point individually by substituting the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values into the equation and seeing if they satisfy it.
1. Checking coordinate [tex]\( (-1, 3) \)[/tex]:
- Substitute [tex]\( x = -1 \)[/tex] into the line equation: [tex]\( y = 2(-1) + 4 \)[/tex]
- Calculate: [tex]\( y = -2 + 4 = 2 \)[/tex]
- The given [tex]\( y \)[/tex]-value is 3, but we calculated it to be 2.
- Therefore, [tex]\( (-1, 3) \)[/tex] does not lie on the line.
2. Checking coordinate [tex]\( (1, 5) \)[/tex]:
- Substitute [tex]\( x = 1 \)[/tex] into the line equation: [tex]\( y = 2(1) + 4 \)[/tex]
- Calculate: [tex]\( y = 2 + 4 = 6 \)[/tex]
- The given [tex]\( y \)[/tex]-value is 5, but we calculated it to be 6.
- Therefore, [tex]\( (1, 5) \)[/tex] does not lie on the line.
3. Checking coordinate [tex]\( (2, 4) \)[/tex]:
- Substitute [tex]\( x = 2 \)[/tex] into the line equation: [tex]\( y = 2(2) + 4 \)[/tex]
- Calculate: [tex]\( y = 4 + 4 = 8 \)[/tex]
- The given [tex]\( y \)[/tex]-value is 4, but we calculated it to be 8.
- Therefore, [tex]\( (2, 4) \)[/tex] does not lie on the line.
4. Checking coordinate [tex]\( (-3, -2) \)[/tex]:
- Substitute [tex]\( x = -3 \)[/tex] into the line equation: [tex]\( y = 2(-3) + 4 \)[/tex]
- Calculate: [tex]\( y = -6 + 4 = -2 \)[/tex]
- The given [tex]\( y \)[/tex]-value is -2, which matches our calculated value.
- Therefore, [tex]\( (-3, -2) \)[/tex] lies on the line.
After checking all points, we conclude that the coordinate that exists on the line [tex]\( y = 2x + 4 \)[/tex] is [tex]\( (-3, -2) \)[/tex].
