Write the equation using function notation.?

Question

Find an equation of the line that passes through (3,-1) and (-2,9) and write the equation using function notation.

Is it F(x) = 2x + 5 ?

Answer 1

m = (9-(-1))/(-2-3) = 10/-5 = -2

-1 = -2(3) + b
b = -1 + 6
b = 5


f(x)= -2x + 5


You got the slope sign reversed. Be careful about that. Otherwise, it's correct!

Answer 2

Yes, the equation is in the form f(x) =. In function notation, f(x) takes the place of y. However, the slope of the line is (y1-y2)/(x1-x2) = (9-(-1))/(-2-3) = 10/-5 = -2, not 2.

Therefore, the equation we have is f(x) = -2x + b.

Plug in 3,-1 for x and f(x) respectively, and x is 5.

So the equation is f(x) = -2x + 5

Answer 3

First you want to find the slope of the line that passes through the points.

m (slope) = (y2 - y1) / (x2 - x1) = change in y over change in x

Fill in the info from your 2 points:
(y2 - y1) / (x2 - x1)
(9 - -1) / (-2 - 3)
10 / -5
-2

The equation for a line is:

y = m(x - x1) + y1

Pick a point and plug in the info. I'll do them both:

Point (3, -1):
y = m(x - x1) + y1
y = -2(x - 3) + -1
y = -2x + 6 - 1
y = -2x + 5

Point (-2, 9):
y = m(x - x1) + y1
y = -2(x - -2) + 9
y = -2x -4 + 9
y = -2x + 5

So the equation of your line should be y = -2x + 5

Answer 4

slope = y2-y1/x2-x1
= 9+1/-2-3
=-2
y=ax+b
9=(-2 x -2) + b
5 = 5
answer = -2x + 5

Answer 5

Don't think so...

m = (9 - -1)/(-2 - 3) = 10/-5 = -2

then

-1 = -2(3) + b
b = 5

So I think it's f(x) = -2x + 5

Answer 6

y-y1/y2-y1=x-x1/x2-x1
=y+1/10=x-3/-5
-5(y+1)=10(x-3)
-5y-5=10x-30
adding 5
-5y=10x-25
dividing by -5
y=-2x+5
f(x)=-2x+5