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

Question

Ive tried to do the problem but i got confused

Answer 1

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

Answer 2

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