Which linear function is represented by the graph?f(x) = –2x + 1f(x) = 1/2–x + 1f(x) = 1/2x + 1f(x) = 2x + 1

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]