To determine if the lines represented by the equations are parallel, perpendicular, or neither, we need to analyze their slopes.
1. The equation of the first line is 5x + y = 7. To find its slope, we can rewrite it in slope-intercept form (y = mx + b), where "m" is the slope:
5x + y = 7
y = -5x + 7
So, the slope of the first line is -5.
2. The equation of the second line is y = -5x - 7. Here, we can see that its slope is also -5.
Now, let's compare the slopes:
- If the slopes of two lines are equal, they are parallel. In this case, both lines have a slope of -5, so they are parallel to each other.
- If the product of the slopes of two lines is -1, they are perpendicular. Here, the product of the slopes (-5 * -5) is 25, which is not equal to -1. Therefore, the lines are not perpendicular.
So, the lines represented by the equations 5x + y = 7 and y = -5x - 7 are parallel to each other.