Answer: (y + 3) = -1/3 (x - 2)
Step-by-step explanation:
Point-slope form has the form of
y - y1 = m (x - x1)
Where
y1 is the y-value of a point on the line
x1 is the x-value of a point on the line
m is the slope of the line
The problem already gives a point on the line, (2, -3)
(y + 3) = m (x - 2)
Remember to put the opposite value of the x and y values. (In other words, do NOT write (y - 3) = m (x + 2) )
The slope of a perpendicular line is the opposite reciprocal of slope of the line it is perpendicular to. The perpendicular line given in the equation is
3x - y = 4
When rearranged to slope-intercept form, we get
y = 3x - 4
Meaning the slope of the perpendicular line is 3. The opposite reciprocal of positive three is negative one-third. Therefore, the slope of the line we are solving for is -1/3.
