To determine whether the line given by the equation [tex]\( y = -1.5x + 6 \)[/tex] intersects or is parallel to the line [tex]\( y = -1.5x \)[/tex], we need to follow these steps:
1. Compare the slopes of the two lines:
The first line is given by [tex]\( y = -1.5x + 6 \)[/tex].
The second line is given by [tex]\( y = -1.5x \)[/tex].
Both lines have the same slope, [tex]\( -1.5 \)[/tex].
2. Understand the implications of the same slope:
Since both lines have the same slope, they are parallel to each other. Parallel lines either coincide (if they are the same line) or never intersect.
3. Determine if the lines coincide or are distinct:
- For the first line [tex]\( y = -1.5x + 6 \)[/tex], the y-intercept is 6.
- For the second line [tex]\( y = -1.5x \)[/tex], the y-intercept is 0.
Since the y-intercepts are different, the lines are distinct and do not coincide.
4. Conclusion:
Because the lines are parallel and distinct, they do not intersect.
Thus, the line [tex]\( y = -1.5x + 6 \)[/tex] does not intersect with the line [tex]\( y = -1.5x \)[/tex] and they are parallel to each other. Therefore, there is no intersection point.
