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write an equation in slope-intercept form for the line who's slope = -5 and passes through (-9,-4)

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3 Answers

Janeen, you have to use point–slope form of linear equation.
y - y1 = m(x - x1)

y - (- 4) = - 5(x - (- 9))

y + 4 = -5(x + 9)

y = - 5x - 45 - 4

y = - 5x - 49
Here is another method of getting the equation of the line that pass through the point     ( -9,-4) and has a slope of -5
 
recall that the slope m = Rise/Run = y2 -y1 / x2 - x1, and (y2-y1)= m (x2-x1)
 
let the point ( -9,-4) be equivalent to ( x2,y2) that is x2=-9, and y2=-4
 
Let the point ( x,y) be equivalent to ( x1,x2) that is x = x1, and y=y1 Now substitute into the equation
above above for m = -5 is the given slope
 
the equation becomes  -4-y = -5(-9-x) and -4-y= 45+5x
 
adding + 4 to to both sides of the equation leads
to - 4+ 4 -y = 45 = 45 + 4 + 5x and -y = 49 + 5x
 
Mutiplying both sides by -1 leads to -(-y) = -( 49+5x) and y= -5x - 49
 
This is the same equation of the form y = mx + b  where m is the slope = -5 and b is
the y intercept = - 49 at x = 0.
 
Please note that your choice of the point in the equation does not affect the end result:
 
Suppose you choose the point (-9,-4) to be ( x1,y1) instead of ( x2,y2)
and the point (x,y) to be ( x2,y2) instead of ( x1,y1)
 
the equation thus becomes y-(-4) = -5 ( x - (-9)) and y + 4 = -5x - 45
 
adding -4 to both sides of the equation leads to y+ 4 - 4 = -5x - 45 - 4,
 
and y = -5x - 49 same as above
Standard equation for a line is Y = mX + b.  Where m is the slope and b is the y intercept.  Since you said that the slope is -5, then m = -5.  Substituting we now have:
 
y = -5X + b,  if we then replace the Y and the X with the values of (-9,-4) we get:
 
-4 = -5(-9) + b,
 
Solving for b.  We get:
 
-4 = 45 + b
 
-49 = b  or  b=-49.
 
So, our equation is Y = -5X - 49.