Question

Which linear function is represented by the graph?

Answer 1

Answer:

$y=-\frac{1}{2}x+1$

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

$slope = \frac{y_2-y_1}{x_2-x_1} =\frac{-1-1}{4-0} =\frac{-1}{2}$

Equation of a line in point slope form is

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

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

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

$y- (1)=-\frac{1}{2}(x-0)$

$y-1=-\frac{1}{2}x$

Add 1 on both sides

$y=-\frac{1}{2}x+1$

Answer 2

Answer:

$f(x)=-\frac{1}{2}x+1$

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

$m=\frac{y2-y1}{x2-x1}$

we have

substitute the values

$m=\frac{-1-1}{4-0}$

$m=\frac{-2}{4}$

$m=-\frac{1}{2}$

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

$m=-\frac{1}{2}$

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

substitute

$f(x)=-\frac{1}{2}x+1$