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Write the equation of the line which passes through (–4, 2) and is parallel to y = –x + 6 in slope-intercept form

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2 Answers

Hi Hannah,
 
They gave you a line (y = -x + 6) which has a slope of -1 (the number in front of the x when the equation is in the form of y = mx + b; in other words, the "m").
 
Another line (the one you are about to find the equation for) is parallel to the above line.  That means the line has the SAME slope, -1. 
 
Now, use the formula y - y1 = m(x - x1) to solve for your answer (x1 and y1 come from the point (-4, 2) ):
 
So,  y - 2 = -1(x - -4)
 
Remember that - -4 is really +4.  After you distribute the -1 you get:
 
y - 2 = -x - 4
   +2        +2
add 2 to both sides to get the final answer
 
y = -x - 2
 
Bill Fanning
El Paso TX
 Always write equation of line :
 
     Y = mX + b   , and then find values of m, b.
 
      
 It is parallel with  line Y = - X + 6
 
     there for m = -1 
 
      Y = -X + b '  
 
   Passes through ( - 4 , 2) , therefore ( -4, 2 ) must be a point on line, and the coordinates should be plugged in the equation:
     2 = - 4 + b , then    b =6
 
   The answer is     Y= -X + 6