Question

Which linear function is represented by the graph?

f(x) = –2x + 1
f(x) = 1/2–x + 1
f(x) = 1/2x + 1
f(x) = 2x + 1

Answer 1

option B is correct.

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

Explanation:

Using Point slope form:

The equation of line is given by:

`y-y_1=m(x-x_1)` .....[1]

where m is the slope of the line and
`(x_1, y_1)` is the point on the coordinate plane.

Consider any two points from the graph:

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

Calculate slope:

Slope is given by:

`m = (y_2-y_1)/(x_2-x_1)`

then substitute the given values we have;

`m = (-1-1)/(4-0)=(-2)/(4)=-(1)/(2)`

Now, substitute the value of m and (0, 1) in [1] then;

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

Simplify:

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

Add 1 to both sides we have;

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

Therefore, the linear function is represented by the graph is

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

Answer 2

Linear function that is represented by the graph is
`y=-(1)/(2)x+1`

Solution-

From the graph,

y - intercept of the linear function is 1 and there are two points on the line (-4, 3), (4, -1)

We can get the equation of line by applying slope-intercept formula,

Slope of the line,

`=(y_2-y_1)/(x_2-x_1)\\\\=(-1-3)/(4+4)\\\\=(-4)/(8)\\\\=-(1)/(2)`

Now applying slope-intercept formula,

`y=mx+c`

Putting the values,

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

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

Therefore, linear function that is represented by the graph is
`y=-(1)/(2)x+1`