Question

Which linear function is represented by the graph?

f(x) = –2x + 1
f(x) = –f(x) equals negative StartFraction one-half EndFraction x plus 1.x + 1
f(x) = f(x) equals StartFraction one-half EndFraction x plus 1.x + 1
f(x) = 2x + 1

Answer 1

`f(x)=-(1)/(2)x+1`

Explanation:

step 1

Find the slope of the linear function

take two points of the graph

(0,1) and (4,-1)

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

we have

substitute the values

`m=(-1-1)/(4-0)`

`m=(-2)/(4)`

`m=-(1)/(2)`

step 2

Find the equation of the linear function in slope intercept form

`f(x)=mx+b`

where

m is the slope

b is the y-intercept

we have

`m=-(1)/(2)`

`b=1` -----> the y-intercept is the point (0,1)

substitute

`f(x)=-(1)/(2)x+1`

Answer 2

`y=-(1)/(2)x+1`

Explanation:

To determine the linear function , pick two points from the given line

(0,1) (4,-1). find the slope using the points

`slope = (y_2-y_1)/(x_2-x_1) =(-1-1)/(4-0) =(-1)/(2)`

Equation of a line in point slope form is

`y-y_1=m(x-x_1)`

slope =-1/2, (0,1)

`y-y_1=m(x-x_1)`

`y- (1)=-(1)/(2)(x-0)`

`y-1=-(1)/(2)x`

Add 1 on both sides

`y=-(1)/(2)x+1`