heres another one, write an equation for the line that is perpendicular to the given line and that contains the given point. 3x + 2y = -10; (-9,-2)
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Perpendicular is a different story. If the orginal line have the slope of 3. Then a new perpendicular line must have a slope of the negative reciprocal. This means that the slope must be -(1/3).
What is the slope of the line 3x + 2y = -10?
If you put it into slope-intercept form, you'll see that
y = (-3/2) x - 5.
So the slope is -3/2.
The slope of a perpendicular line to 3x + 2y = -10
must then have slope 2/3 (the negative reciprocal of -3/2).
So then we want this perpendicular line to pass through (-9, -2).
So we can use “point-slope” form of a line:
y – y1 = m*(x – x1).
So y – (-2) = (2/3) * (x – (-9)).
Simplify to get the equation of the line which is
perpendicular to your first line and going through the point (-9, -2).