how do I write an equation of the line containing the specified point and perpendicular to the indicated line

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

To write an equation of the line that is perpendicular to the given line and passes through the specified point, you need to follow a few steps:

1. Get the slope of the given line: To find the slope of the given line, you need to rearrange the equation into slope-intercept form, which is y = mx + b, where m represents the slope. In this case, the given equation is x - 2y = 3. Rewrite the equation in slope-intercept form by isolating y.

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

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

2. Find the slope of the line perpendicular to the given line: Perpendicular lines have slopes that are negative reciprocals of each other. To find the slope of the line perpendicular to the given line, take the negative reciprocal of the original slope. The negative reciprocal of 1/2 is -2.

3. Use the point-slope form to write the equation: You now have the slope (-2) and a specified point (-2, -5). To write the equation of the line, you can use the point-slope form, which is y - y1 = m(x - x1), where (x1, y1) represents the given point.

Plug in the values into the point-slope form equation:

y - (-5) = -2(x - (-2))
y + 5 = -2(x + 2)
y + 5 = -2x - 4
y = -2x - 4 - 5
y = -2x - 9

Therefore, the equation of the line that contains the specified point (-2, -5) and is perpendicular to the given line x - 2y = 3 is y = -2x - 9.