Question

Find the equation of the line that is parrallel to y=-x+9 and contains the point (7,-13)

Answer 1

• 
  `\rm{y=-x-6}`

Explanation:

Parallel lines have the same slope. So the slope of the line that's parallel to

• 
  `\sf{y=-x+9}` is
• 
  `\sf{-1}`

Now, plug that into the Point-slope formula:

• 
  `\rm{y-y_1=m(x-x_1)}`

Where:

• 
  `\rm{y_1}` is the y-coordinate of the point
• 
  `\rm{m}` is the slope
• 
  `\rm{x_1}` is the x-coordinate of the point

Plug in the values:

• 
  `\rm{y-(-13)=-(x-7)}`
• 
  `\rm{y+13=-(x-7)}`
• 
  `\rm{y+13=-x+7}`
• 
  `\rm{y=-x+7-13}`
• 
  `\rm{y=-x-6}`

I hope this helps!!

Answer 2

y = - x + 6

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - x + 9 ← is in slope- intercept form

with slope m = - 1

• Parallel lines have equal slopes , then

y = - x + c ← is the partial equation of the parallel line

to find c substitute (7, - 13 ) into the partial equation

- 13 = - 7 + c ⇒ c = - 13 + 7 = - 6

y = - x + 6 ← equation of parallel line