What equation has a graph perpendicular to the graph of
5x = 20y - 12?
A. y = -4x + 2
B. y = -1/4x - 5/3
C.y = 4x+1
D. y = 1/4× + 3/5
To determine the equation that has a graph perpendicular to the graph of 5x = 20y - 12, we need to find the slope of the given graph and then find the negative reciprocal of it.
Rearranging the given equation, we can rewrite it as y = (5/20)x + 12/20.
Simplifying, we have y = (1/4)x + 3/5.
The slope of the given graph is 1/4.
The negative reciprocal of 1/4 is -4.
So, the equation with a graph perpendicular to the given graph should have a slope of -4.
Now, we can examine the options.
A. y = -4x + 2
The slope of this equation is -4, which matches with our expectation. This could be the correct answer.
B. y = -1/4x - 5/3
The slope of this equation is -1/4, which is not the negative reciprocal of 1/4. This is not perpendicular to the given graph.
C. y = 4x+1
The slope of this equation is 4, which is not the negative reciprocal of 1/4. This is not perpendicular to the given graph.
D. y = 1/4× + 3/5
The slope of this equation is 1/4, which is not the negative reciprocal of 1/4. This is not perpendicular to the given graph.
So, the equation that has a graph perpendicular to the graph of 5x = 20y - 12 is y = -4x + 2.
Therefore, the answer is A. y = -4x + 2.