The graphs of y = -4x and y = -4x + 2 are shown. Use the drop-down menus to complete the statements. The ratios of y x are the same for the graph of The ratios of y x are NOT the same for the graph of

Let’s break down the question step by step.

1. The first equation is ( y = -4x ). This represents a linear function with a slope of -4 and no y-intercept (it crosses the origin).

2. The second equation is ( y = -4x + 2 ). This is also a linear function with the same slope of -4 but has a y-intercept of 2, meaning it crosses the y-axis at the point (0, 2).

Now, let’s examine the ratios of ( frac{y}{x} ):

– For the graph of ( y = -4x ):

– The ratio ( frac{y}{x} = frac{-4x}{x} = -4 ) (for any nonzero x).

– For the graph of ( y = -4x + 2 ):

– At any point on this line, the ratio ( frac{y}{x} ) changes depending on the value of x because of the constant term (+2). For example, if ( x = 1 ), ( y = -4(1) + 2 = -2 ), so ( frac{y}{x} = frac{-2}{1} = -2). If ( x = 2 ), ( y = -4(2) + 2 = -6), thus ( frac{y}{x} =