To determine the relationship between the graphs of the equations 5x-3y = -5 and 2x-y = 8, we can compare their slopes. The slope of a linear equation is the coefficient of x when the equation is written in slope-intercept form (y = mx + b).
Let's rewrite the equations in slope-intercept form:
5x-3y = -5
-3y = -5 - 5x
y = (5/3)x + 5/3
2x-y = 8
-y = -8 - 2x
y = 2x + 8
By comparing the coefficients of x, we can see that the slope of the first equation is 5/3 and the slope of the second equation is 2.
If two lines have different slopes, they are not parallel. If the product of their slopes is -1, they are perpendicular.
In this case, the slopes are not equal and their product is not -1. Therefore, the graphs of the two equations are intersecting but not perpendicular.
Hence, the correct answer is: intersecting but not perpendicular.