Identify an equation in point-slope form for the line parallel to y=- 2/3x +8 that passes through (4,-5)

H(x) = (-2/3)*x - 7/3

Explanation: If you have a linear equation y = ax + b, all the parallel lines of y are of the form P = ax + c

so all the paralel lines have the same slope.

Now, we have y = -2/3*x + 8

so we want to find a function of the shape:

H = -2/3*x + c

that pases through the point (4, - 5)

this means:

-5 = -(2/3)*4 + c

c = - 5 + 8/3 = (-15 + 8)/3 = -7/3

So the equation is:

H(x) = (-2/3)*x - 7/3

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