3. find the equation in point-slope form of the lines through point p(2.0) that are a) parallel to, and b)
perpendicular to the line x +2y = 3.

a) y = -0.5(x - 2)

b. y = 2(x - 2).

Step-by-step explanation:

Consider the given line:

x + 2y = 3

2y = -x + 3

y = -0.5x + 1.5

So the slope of this line is -0.5.

(a) Parallel to the given line: we need an equation with slope = -0.5 and passing through the point (2,0).

Point-slope form is y - y1 = m(x - x1) so we have:

y - 0 = -0.5(x - 2)

y = -0.5(x - 2)  (answer).

(b)  The line perpendicular to  the given line will have a slope of -1 / -0.5 = 2.

So our equation is

y - 0 = 2(x - 2)

y = 2(x - 2)   (answer).

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