Respuesta :

InesWalston

Answer-

Linear function that is represented by the graph is [tex]y=-\dfrac{1}{2}x+1[/tex]

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,

[tex]=\dfrac{y_2-y_1}{x_2-x_1}\\\\=\dfrac{-1-3}{4+4}\\\\=\dfrac{-4}{8}\\\\=-\dfrac{1}{2}[/tex]

Now applying slope-intercept formula,

[tex]y=mx+c[/tex]

Putting the values,

[tex]\Rightarrow y=-\dfrac{1}{2}x+1[/tex]

[tex]y=-\dfrac{1}{2}x+1[/tex]

Therefore, linear function that is represented by the graph is [tex]y=-\dfrac{1}{2}x+1[/tex]

Answer:

option B is correct.

[tex]y =\frac{1}{2}(-x)+1[/tex]

Step-by-step explanation:

Using Point slope form:

The equation of line is given by:

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

where m is the slope of the line and [tex](x_1, y_1)[/tex] 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:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

then substitute the given values we have;

[tex]m = \frac{-1-1}{4-0}=\frac{-2}{4}=-\frac{1}{2}[/tex]

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

[tex]y-1=-\frac{1}{2}(x-0)[/tex]

Simplify:

[tex]y-1=-\frac{1}{2}x[/tex]

Add 1 to both sides we have;

[tex]y =\frac{1}{2}(-x)+1[/tex]

Therefore, the linear function is represented by the graph is

[tex]y =\frac{1}{2}(-x)+1[/tex]

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