find an equation of the line that contains (4,-9) and is parallel to the line that contains (-4,8) and (8,-1)

Question

slope not provided need an equation form

Answer 1

Hi Mary,

 

Lines that are parallel have the same slope. Therefore, we need to determine the slope, "m", for the line that contains (-4,8) and (8,-1). The equation for this is

 

   m = (y₁ - y₂) / (x₁ - x₂), where "1" and "2" are our two given points.

 

Therefore, we have

 

   m = (8 - -1) / (-4 - 8) = 9/-12 = -3/4

 

Now that we have "m", we can look at several other posts that take it from there. For example

 

http://www.wyzant.com/resources/answers/4293/find_an_equation_for_the_line_parallel

 

http://www.wyzant.com/resources/answers/5545/graph_a_line_parallel_to_2x_4y_5

 

are a couple of fine answers. So I'll let you take it from here.

 

Good luck !

 

 

Answer 2

Hi Mary,

I think I can help you with this. I don't know how much you know already so I'll explain each step.

 

Lets call the line that contains (4,-9), line 1 and let's call the line that is parallel to this, line 2

 

Because the two lines are parallel this means they both have the same slope. So if we find the slope of line 2 then we then know the slope of line 1.

 

So lets look at line 2 which contains (-4, 8) and (8,-1).  We use these points in the slope formula,

m=(y₂-y₁)/(x_2-x₁). [m is used to represent slope]

 

Remember that a point is usually in the form (x,y).

In this case, because there are 2 points we need to tell the difference between the two x's and the two y's so we label them (x₁,y₁) and (x₂,y₂). ,

[When I'm working a problem, I usually write the label for each number, x₁, y₁, x₂, y₂, above it to keep from getting mixed up.]

 

In this case x₁ is -4, y₁ is 8, x₂ is 8, and y₂ is -1.

Plug those in to the formula and solve for m.

m=(y₂-y₁)/(x₂-x₁) becomes

m=((-1)-8)/(8-(-4)).

[note that I put the negative numbers inside of parenthesis to keep from getting confused]

 

Remember your order of operation and do any addition or subtraction first.

(-1)-8=-9

 

8-(-4) becomes 8+4 and 8+4=12

 

m=((-1)-8)/(8-(-4)) becomes

 

m=(-9)/(12)

 

We keep this answer as a fraction but reduce the fraction.

 9 and 12 are both divisible by 3.

 

so m= -3/4

 

This is our slope for both line 1 and line 2

 

We can now use the Point/Slope Formula to find the equation of the line for line 1

 

 y-y₁= m (x-x₁)

In this case the (x₁, y₁) is refering to the point that line 1 contains and m is the slope we just found.

x₁ is 4 and y₁ is -9

 

y-y₁   =   m (x-x₁) becomes

y-(-9)=(-3/4)(x-4)

 

simplify and foil

 

y-(-9)=(-3/4)(x-4) becomes

y+9   = -3/4x - (-3/4)(4) becomes

 

y+9   = -3/4x - (-3) becomes

 

y+9 = -3/4x+3

 

subtract 9 from both sides

 

y+9-9=-3/4x+3-9 becomes

 

y = -3/4x-6

 

You have now found the slope intercept form of the equation of the line y=mx+b.

[so called because we can easily use it to find both the slope m and the y-intercept (0,b)]

 

I hope that answers your question.

Debra A.