How can you determine if two lines are perpendicular? How can you tell if two lines are parallel? State whether the following sets of lines are parallel, perpendicular or intersecting. Then explain why.
1) y = x + 4
y = x - 3
2) y = 3x - 7
y = -1/3 x + 10
3) y = 3x -7
y = -3x + 10
To determine if two lines are perpendicular, you need to check if their slopes are negative reciprocals of each other. The slope of a line is given by "m" in the equation y = mx + b, where "m" represents the slope. If the slopes of two lines, say m1 and m2, are negative reciprocals of each other, i.e., m1 * m2 = -1, then the lines are perpendicular.
To determine if two lines are parallel, you need to check if their slopes are equal. If the slopes of two lines, m1 and m2, are equal, then the lines are parallel.
Now let's analyze the sets of lines you provided:
1) y = x + 4
y = x - 3
Both lines have a slope of 1, which means the slopes are equal. Therefore, the lines are parallel.
2) y = 3x - 7
y = (-1/3)x + 10
The slope of the first line is 3, and the slope of the second line is -1/3. Since the slopes are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular. They will intersect at a point.
3) y = 3x - 7
y = -3x + 10
The slope of the first line is 3, and the slope of the second line is -3. Since the slopes are negative reciprocals of each other (3 * -3 = -9 = -1), the lines are perpendicular.