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

Question

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

Answer 1

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

Answer 2

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

Answer 3

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.