91Ó°ÊÓ

Perpendicular lines are lines that intersect at a right angle, which is 90 degrees. This characteristic makes them very important in geometry and algebra.
To determine if two lines are perpendicular, we need to look at their slopes. The slopes of two perpendicular lines are negative reciprocals of each other. What does a negative reciprocal mean? It means that if the slope of one line is 'a/b', the slope of the line perpendicular to it will be '-b/a'.
In our problem, the original line had a slope of 1. The negative reciprocal of 1 is -1. Therefore, any line perpendicular to our original line will have a slope of -1.

The slope-intercept form of a linear equation is a very useful way to express the equation of a line. It is written as: y = mx + bwhere:

• y is the dependent variable
• m is the slope of the line
• x is the independent variable
• b is the y-intercept (the point where the line crosses the y-axis)

This form allows us to quickly identify both the slope and the y-intercept of the line. For example, in the equation from our exercise, we rearranged and simplified it to get y = x + 7/3, where the slope (m) is 1 and the y-intercept (b) is 7/3.
Knowing the slope and intercept immediately tells us a lot about the line's behavior and position on a graph.

The concept of a negative reciprocal is fundamental when dealing with perpendicular lines. The negative reciprocal of a number is found by flipping the number's numerator and denominator and then changing the sign. For example, the negative reciprocal of 3 (which can be written as 3/1) is -1/3.
If you know the slope of a line, you can find the slope of a perpendicular line by taking its negative reciprocal. This is because perpendicular lines have slopes that multiply to -1. For instance, if one line has a slope of 2/3, a line perpendicular to it will have a slope of -3/2.
In our exercise, the original slope was 1. The negative reciprocal of 1 is -1, making it straightforward to determine that a perpendicular line would have a slope of -1.