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

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 +

Now we have a slope and a point... we can use them to find the b (y-intercept)
x = 4, y = 3, and m = 


Using the common denominator fraction for 3, we subtract 4/3 from both sides


plug the values for m and b into the slope intercept form

Geometric pattern of 2 i’m guessing. not really sure about what you’re asking but i hope this !