Find the equation for the line that passes through the point (−3,−3), and that is perpendicular to the line with the equation x=4.

First we have to find the slope of the line that's given, y - 4 = 2(x+2). The slope is 2 (if we multiply 2*x we would get 2x and the 2 is the slope).

Two lines are perpendicular if their slopes are negative reciprocals. So if the first line has a slope of 2, a perpendicular line would have a slope of -1/2

Now we have to find the equation for the line with slope of -1/2 that passes through the point (3,3). If we use the point-intercept form we can write it as:

y = mx + b

Since the slope is -1/2 and we know that when x = 3, y = 3 (since the line passes through that point) we can substitute the values and solve for b

y = mx+b

3 = -1/2 *3 + b

3 = -3/2 + b

3 = -11/2 + b

41/2 = b

Now we can write the equation as

y = -1/2x + 41/2

. + λrh() e 1 1 2 4 4 4 4 4 3 4 4 4 4 4 + th−1(− s(x)2 dx ω + λrh−1() e 2 1 2 4 4

step-by-step explanation: