Question

write the slope intercept form of an equation of the line that passes through (4,3) that is perpendicular to the line Y=-3x-15

Answer 1

If two lines are perpendicular, then their slopes have a product of -1 or you could say they are opposite signed reciprocals of each other.
The given equation has a slope of -3.  We know this because it is in slope-intercept form y = mx + b ...y = (slope)x + (y-intercept).

so taking the slope -3...the opposite signed reciprocal would be +$\frac{1}{3}$

Now we have a slope and a point... we can use them to find the b (y-intercept)
x = 4, y = 3, and m = $\frac{1}{3}$
$3= \frac{1}{3} (4)+b$
$3= \frac{4}{3} +b$
Using the common denominator fraction for 3, we subtract 4/3 from both sides
$3= \frac{9}{3}$
$\frac{5}{3} =b$
plug the values for m and b into the slope intercept form
$y= \frac{1}{3} x+ \frac{5}{3}$