Question

using point-slope form, write the equation of the line that passes through (-3,2) and has a slope of 5

Answer 1

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

Answer 2

y-2=5(x-(-3))

or

y-2=5(x+3)

(they represent the same thing)