SOLUTION: What would the equation be of this line if it were rotated to be half as steep and the y-intercept was kept the same? Y=-8x+7
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Question 1015335: What would the equation be of this line if it were rotated to be half as steep and the y-intercept was kept the same? Y=-8x+7 Answer by Theo(13342) (Show Source):
if you are talking about half the slope, then the new slope will be -4 rather than -8.
if you are talking about half the angle, you would have to do the following.
if the slope is -8, then the angle would be tan(-8) = -82.8749... degrees.
half of that angle would be -41.4374... degrees.
tan of -41.4374... degrees is equal to -.8827...
your new equation would be y = -.8827822185x + 7 which i rounded to y = -.88x + 7 since you couldn't see the difference on the graph.
the y-intercept remains the same at 7.
this is because slope intercept form of the equation of a straight line is y = mx + b.
m is the slope
b is the y-intercept.
in your original equation of y = -8x + 7, ...
m is equal to -8
b is equal to 7.
in your first revised equation of y = -4x + 7, ...
m is equal to -4
b is equal to 7.
in your second revised equation of y = -.88x + 7, ...
m is equal to -.88
b is equal to 7.
here's a graph of all 3 equations.
the red line is the original equation of y = -8x + 7.
the blue line is the first revised equation of y = -4x + 7.
the orange line is the second revised equation of y = -.88x + 7
halving the slope did not make anywhere near as dramatic a change as halving the angle of deflection.
half as steep could be interpreted as half the angle of deflection.
i'm not sure what your instructor expects.
if you're dealing with slopes, than maybe half the slope is the correct answer.
check with your instructor to see which one of these he's looking for.
