Point slope form

Question

What is the equation in point slope form for the line parallel to y=5x - 4 that contains P (-6,1)? 

 

A. X - 1 =-5(y + 6)

 

B. Y +1 = 5(x + 6)

 

C. Y - 1 = -5(x + 6) 

 

D. Y - 1 = 5(x + 6) 

Answer 1

The slope must match the original slope of 5, so options A and C are out (A has slope of -1/5 and C has a slope of -5). Also, notice that the point slope form makes it really obvious that point (1,-6) is on A, (-6,-1) is on B, and (-6,1) is on C and D. Thus, B is incorrect, because the line can't go through (-6,-1) and (-6,1) while having a slope of 5.

 

If that second part is confusing, the point (-6,1) must be on the line. Try B:

(1)+1 =?= 5(-6+6)

2 =?= 0

nope. So, D. Check it.

(1)-1 =?= 5(-6+6)

0 =?= 0

yep!

 

D

Answer 2

y = mx + b

 

m = 5 since parallel to y = 5x-4

 

1 = -6(5) +  b, so b = 31

 

y = 5x + 31, which is the same as y - 1 = 5x + 30 = 5(x + 6)

 

y - 1 = 5(x + 6), which is answer (D).

Answer 3

Point slope form is

 

y - y₁ = m(x - x₁)

 

where:

m = slope

(x₁ , y₁) = given point

 

 

Sine the line is parallel, the slope remains as 5.  Then plug in these values into the form.

 

m = 5

x₁ = -6

y₁ = 1