Hello, I would like help on how to solve this.
Determine whether the graphs of the given equations are parallel, perpendicular, or neither.
y = x + 11.
y = - x =2.
the slopes are different, so the lines are not parallel.
Their product is -1, so the lines are perpendicular.
To determine whether the graphs of the two equations are parallel, perpendicular, or neither, we need to analyze their slopes.
The slope-intercept form of a linear equation is written as y = mx + b, where m represents the slope of the line.
For the equation y = x + 11, we can see that the coefficient of x is 1. Therefore, the slope of the line represented by this equation is 1.
Now, let's analyze the equation y = -x + 2. Here, the coefficient of x is -1, indicating that the slope of this line is -1.
Since these slopes are not the same, the lines represented by these equations are not parallel.
To determine if they are perpendicular, we can utilize the fact that the product of the slopes of two perpendicular lines is always -1. In this case, the product of the slopes -1 and 1 is indeed -1.
Therefore, the graphs of the given equations are perpendicular to each other.
In summary, to determine whether the graphs of two equations are parallel, perpendicular, or neither, compare the slopes of the lines represented by the equations. If the slopes are the same, the lines are parallel. If the product of the slopes is -1, the lines are perpendicular. If neither of these conditions is met, the lines are neither parallel nor perpendicular.