write an equation of the line containing the specified point and perpendicular to the indicated line
(-2,-5), x-2y=3
change it to slope intercept form
y=1/2 x-3/2
now a line parallel is y=mx+b where m=1/2
y= 1/2 x + b Put in your x,y given, and solve for b.
thank you
To find the equation of a line that is perpendicular to another line, we need to know that the slopes of perpendicular lines are negative reciprocals of each other.
The given line's equation is x - 2y = 3. To find its slope, we need to rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope:
x - 2y = 3
-2y = -x + 3
y = (1/2)x - 3/2
The slope of the given line is 1/2. Since the line we want is perpendicular, the slope of our line will be the negative reciprocal of 1/2, which is -2.
Now we have the slope (-2) and a point (-2, -5) that lies on the line. We can use the point-slope form of a line (y - y1 = m(x - x1)) to find the equation:
y - (-5) = -2(x - (-2))
y + 5 = -2(x + 2)
Expanding:
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.