write an equation of the line containing the specified point and perpendicular to the indicated line?

(-2,-5),x-2-2y=3

x -2 -2y= 3

x -5 = 2y
y = x/2 -5/2 The slope is 1/2, so the perpendicular slope to it would be -2.

For me, I find it easier to draw a graph. Find point (-2, -5) and draw a line with slope of -2. Once you hit the y-axis, the number on the axis is you're y-intercept. So the equation should be y = -2x -6

y = .5x -2.5 or y= 1/2x -5/2

So the slope of your line is -2
y+5=-2(x+2) y= -2x-4-5 y=-2x-9

And the winner is . . . the one which contains the given point.

-2(-2) - 6 = 4-6 = -2 Bzzt!
-2(-2) - 9 = 4 - 9 = -5 Ding Ding!

To find the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line and then apply the concept that the slopes of perpendicular lines are negative reciprocals of each other.

First, let's rewrite the given equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. We'll isolate y in the equation x - 2 - 2y = 3:

x - 2 - 2y = 3
-2y = -x + 5
y = (1/2)x - 5/2

From this equation, we can see that the slope of the given line is 1/2.

To find the slope of the line perpendicular to this, we can take the negative reciprocal of 1/2. Inverting 1/2 gives us 2/1 (or simply 2), and changing the sign gives us -2.

Now, we have the slope (-2) and a point (-2, -5). We can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is given by y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope:

Plugging in the values, we have:
y - (-5) = -2(x - (-2))

Simplifying further:
y + 5 = -2(x + 2)

Distributing -2 to both terms inside the parentheses:
y + 5 = -2x - 4

Finally, rearranging the equation to slope-intercept form gives:
y = -2x - 9

So, the equation of the line containing the point (-2, -5) and perpendicular to the line x - 2 - 2y = 3 is y = -2x - 9.