*point–slope form*of linear equation.

*y - y*

_{1}= m(x - x_{1})y - (- 4) = - 5(x - (- 9))

y + 4 = -5(x + 9)

y = - 5x - 45 - 4

**y = - 5x - 49**write an equation in slope-intercept form for the line who's slope = -5 and passes through (-9,-4)

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

y + 4 = -5(x + 9)

y = - 5x - 45 - 4

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:

Solving for **b**. We get:

So, our equation is **Y = -5X - 49.**

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