y-2=5(x-(-3))
or
y-2=5(x+3)
(they represent the same thing)
Slope, m=5
And, the line passes through (-3,2)
The point-slope form of line is:y=mx+b
m=5, as slope is 5
x=-3
y=2
as point is (-3,2)
So, Let us plug x=-3, y=2 and m=5 in y=mx+b
y=5x+b
2=5(-3)+b
When we plug x=-3 in y=mx+b
5 gets multiplied to -3
5*-3=-15
2=-15+b
To solve for b, we must isolate b
That is, we try to get rid of -15 from right side
So, Let us add 15 on both sides
2+15=-15+b+15
17=0+b
So, 17=b
Or, b=17
So, the equation that has slope=5, and passes through point (-3,2) has b=17
So, the equation in y=mx+b form is
y=5x+17
So, the required equation:
y=5x+17
