write an equation of the line containing the specified point and perpendicular to the indicated line (-2,-5), x-2y=3
To find the equation of a line perpendicular to a given line, we need to determine the slope of the given line.
First, we will rewrite the given line equation, x - 2y = 3, in slope-intercept form, which is y = mx + b, where m represents the slope:
Starting with x - 2y = 3:
-2y = -x + 3
y = (1/2)x - 3/2
From this equation, we can deduce that the slope of the given line is 1/2.
Since a line perpendicular to another line has a slope that is the negative reciprocal of the original slope, the slope of the new line will be -2 (negative reciprocal of 1/2).
Now that we have the slope (-2) and a point (x, y) = (-2, -5), we can use the point-slope form of a line to write the equation:
y - y1 = m(x - x1)
Plugging in the values, we get:
y - (-5) = -2(x - (-2))
y + 5 = -2(x + 2)
Expanding and simplifying further:
y + 5 = -2x - 4
y = -2x - 4 - 5
y = -2x - 9
Therefore, the equation of the line containing the point (-2, -5) and perpendicular to the line x - 2y = 3 is y = -2x - 9.