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write an equation in slope intercept form through the given point with the given slope(10,-9) m=-2

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2 Answers

When generalized, slope-intercept form is: y = m x + b
We have the slope, m = -2, but we still need the y-intercept, b, to complete the equation.
 
But we do have a point on the line, (10,-9). And if that point is on the line, it must satisfy the equation.
So it must be true that:
(-9) = -2(10) + b    [multiply]
-9 = -20 + b    [add 20]
11 = b
 
Now we know both the slope, m = -2, and the y-intercept, b = 11;
so our equation is: y = -2x + 11
 
 
Hi Tom;
Christopher's Answer was excellent.  I would like to add to it.
slope-intercept form is...
y=mx+b, m is the slope, b is the y-intercept, the value of y when x=0.
Another equation is point-slope...
y-y1=m(x-x1)
When applying the slope and one point provided, this equation will expand into slope-intercept form...
y--9=(-2)(x-10)
y+9=-2(x-10)
y+9=-2x+20
Let's subtract 9 from both sides...
-9+y+9=-2x+20-9
y=-2x+11