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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

Which linear function is represented by the graph fx 2x 1 fx fx equals negative StartFraction onehalf EndFraction x plus 1x 1 fx fx equals StartFraction onehalf class=

Respuesta :

calculista

Answer:

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

Step-by-step 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

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

substitute the values

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

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

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

step 2

Find the equation of the linear function in slope intercept form

[tex]f(x)=mx+b[/tex]

where

m is the slope

b is the y-intercept

we have

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

[tex]b=1[/tex] -----> the y-intercept is the point (0,1)

substitute

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

Answer:

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

Step-by-step explanation:

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

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

[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{-1-1}{4-0} =\frac{-1}{2}[/tex]

Equation of a line in point slope form is

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

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

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

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

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

Add 1 on both sides

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

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