To determine the slope of a line that is perpendicular to another line, we first need to understand the slope of the line described by the equation y = 2x + 5.
The equation is in the slope-intercept form, which is y = mx + b, where m represents the slope and b is the y-intercept. From the equation y = 2x + 5, we can see that the slope (m) is 2.
Now, when two lines are perpendicular, the slopes of those lines are negative reciprocals of each other. In other words, if the slope of one line is m, the slope of the line that is perpendicular to it will be -1/m.
Given that the slope of our line is 2, we can find the slope of the perpendicular line:
- Calculate the negative reciprocal:
- Slope of perpendicular line = -1/2
Thus, the slope of the line that is perpendicular to the line represented by the equation y = 2x + 5 is -1/2.