To determine which equation has a graph perpendicular to the given equation, we need to find the slope of the given equation and then find the equation with the negative reciprocal slope.
The given equation is 7x = 14y - 8. To put it in slope-intercept form (y = mx + b), we divide both sides by 14:
(7/14)x = (14/14)y - 8/14
(1/2)x = y - 4/7
y = (1/2)x + 4/7
The slope of this equation is 1/2.
To find the equation with the negative reciprocal slope, we flip the fraction and change its sign:
-1/2
Out of the given options:
y = -2x - 7 has a slope of -2, which is not the negative reciprocal of 1/2.
y = -1/2x + 4 has a slope of -1/2, which is the negative reciprocal of 1/2.
y = 1/2x + 1 has a slope of 1/2, which is not the negative reciprocal of 1/2.
y = 2x + 9 has a slope of 2, which is not the negative reciprocal of 1/2.
Therefore, the equation that has a graph perpendicular to 7x = 14y - 8 is y = -1/2x + 4.
Which equation has a graph perpendicular to the graph of 7x = 14y – 8? explain your work.
y = –2x – 7
y = – 1/2x + 4
y = 1/2x + 1
y = 2x + 9
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