Finding the equation of a line...?

Question

ok i know i should know this, but for some reason i forget.

how do you find the equation of a line from a given point

(let's say... 0, -1)

and the slope.

(how about...-1)

i know y=mx + b, but I can't figure out how to get the whole equation, and i have like 10 questions on it.

please remind me how!!

thanks!

Answer 1

first because you have a point and a slope put it in point slope form:

y-y1=m(x-x1) where m=slope and y1 means the y of the point, same for x

so w/ your example:

y-(-1)=-1(-x-0)

distribute and simplify...

y+1=x

put the 1 over with the x so y will be alone

y=x+1

remember, when an equation just has -x, it means the slope is -1.

so, there's your answer in slope intercept form!

Answer 2

Ok the reason you forget is because you're missing the other equation:

y-y1=m(x-x1) where (x1,y1) is the point that you have and m is the slope. Just substitute what you have there and distribute the slope and combine like terms to make it look like y=mx +b

Answer 3

You plug in your known point and your known slope to find b

Using your example,

y=mx+b

-1=(-1)*0+b

-1=0+b

-1=b

So the equation is y=(-1)*x+(-1)

Or y=-x-1

_/

Answer 4

Line equation:

y = mx + b

m = slope

b = y-intercept

----------------------

Given: Slope of -1

Means: m = -1

Plug this into the formula.

y = mx + b

y = (-1)x + b

y = -x + b

Given: Point (0, -1)

Means: x = 0, y = -1

Plug these known x and y values into the equation you have so far and solve for b.

y = -x + b

-1 = -(0) + b

-1 = b

Plug this into the formula to get the final equation.

y = -x + b

y = -x + (-1)

y = -x - 1

Hope this helped!