Which equation has a graph perpendicular to the graph of 7x = 14y – 8 ? (1 point) Responses y = –2x – 7 y = –2 x – 7 y = –x + 4 y = – Image with alt text: one-half x + 4 y = x + 1 y = Image with alt text: one-half x + 1 y = 2x + 9 y = 2 x + 9
To determine which equation has a graph that is perpendicular to the given equation, we need to find the slope of the given equation first. The given equation is 7x = 14y - 8.
To put this equation in slope-intercept form (y = mx + b), we can divide both sides by 14:
7x/14 = (14y - 8)/14
x/2 = y - 8/14
x/2 = y - 4/7
Comparing this equation with y = mx + b, we can see that the slope of the given equation is 1/2. The slope of a line perpendicular to this line would be the negative reciprocal of the slope, which is -2.
Among the given options, the equation with a slope of -2 is y = -2x - 7. Thus, the correct equation is y = -2x - 7.