write an equation in point-slope form of the line through point J(4,1) with slope -4.

Question

geometry ... write an equation in point-slope form of the line through point J(4,1) with the slope -4.

 

Answer 1

Hi Jeni;

(y-y₁)=m(x-x₁)

(y-1)=(-4)(x-4)

y-1=-4x+16

Let's add 1 to each side to isolate y...

1+y-1=-4x+16+1

y=-4x+17

The equation is now in the form of slope-intercept.

y=mx+b

m=slope

b=y-intercept, the value of y when x=0.

 

Or we can take the point-slope equation and do something else...

y-1=-4x+16

Let's separate the constant from the variables...

Let's add 4x to both sides...

4x+y-1=-4x+16+4x

4x+y-1=16

Let's add 1 to both sides...

1+4x+y-1=16+1

4x+y=17

The equation is now in the form of standard formula.

Ax+By=C, A≥0

Because A=4, it is greater than zero.  We have no additional work to do.