dtermine the linear function whose graph is a line with a slope of 2 and contains the point (4, - 1)?

Answer 1

Slope Intercept form

y = mx + b

-1 = 2(4) + b

-1 = 8 + b

- 1 - 8 = 8 + b - 8

- 9 = b

- - - - - - -
The equation

y = 2x - 9

- - - - - - - -s-

Answer 2

There are two ways to do this problem. The first is to make a graph and plot the point (4,-1) and then give it a slope of 2. The second is to solve it algebraically

Since I very well can't show you a graph, ill show you how to do it the algebraic way.

The equation for a line will be in the form y=mx+b

m= slope
b=y intercept (what y equals when x=0)

Since you have already been provided with a slope, you can put it into the equation quickly.

y=2x+b

Now we just need the b, which isnt that hard to find. To find b, plug the point (4,-1) you were given into the equation. Replace the y with -1 since -1 is the y value. Replace x with 4.

Now you have:

-1=2(4)+b

now you can solve for "b"

b=-9

so you get the equation y=2x-9

Answer 3

To start, you need the point-slope formula,

y - y1 = m(x - x1)

*The ones are subscripts.

The ordered pair represents those x1 and y1 values, and m is your slope... so if you plug them into the formula,

y - (-1) = 2(x - 4)

y + 1 = 2x - 8

y = 2x - 9

...This is your linear function (since x is raised to only a power of 1).

Answer 4

3.) m = 3/4 x = - 3 y = a million b = y - mx ........ (Derived from y = mx + b) b = a million - 3/4(- 3) b = a million - 9/4 b = 4/4 - 9/4 b = - 5/4 Equation: y = 3/4 x - 5/4 ¯¯¯¯¯¯¯¯¯¯¯¯ 4.) x1 = - a million y1 = - 2 x2 = a million y2 = - 10 m = (y2 - y1) / (x2 - x1) m = [- 10 - (- 2)] / [a million - (- a million)] m = (- 10 + 2) / (a million + a million) m = - 8/2 m = - 4 b = y1 - m(x1) b = - 2 - [- 4(- a million)] b = - 2 - 4 b = - 6 Equation: y = - 4x - 6 ¯¯¯¯¯¯¯¯¯¯    

Answer 5

slope = (y2 - y1)/(x2 - x1)
2 = (y - (-1))/(x - 4)
2 = (y + 1) / (x - 4)
2(x - 4) = y + 1
y = 2x - 9

Answer 6

F(X)= 2X + C
- 1 = 2(4) + C , C= -9
F(X)= 2X - 9