20 POINTS!Use the graph of the line to answer the questions.1. What is an equation of the line in point-slope form?2. How can the point-slope form be written in function notation?

Accepted Solution

Answer:[tex]y+1=\dfrac{1}{3}(x+2)[/tex] - point-slope form[tex]f(x)=\dfrac{1}{3}x-\dfrac{1}{3}[/tex] - function notationStep-by-step explanation:The point-slope form of an equation of a line:[tex]y-y_1=m(x-x_1)[/tex]m - slopeThe formula of a slope:[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]From the graph we have the points (-2, -1) and (1, 0).Substitute:[tex]m=\dfrac{0-(-1)}{1-(-2)}=\dfrac{1}{3}[/tex][tex]y-(-1)=\dfrac{1}{3}(x-(-2))[/tex][tex]y+1=\dfrac{1}{3}(x+2)[/tex] - point-slope form[tex]y+1=\dfrac{1}{3}(x+2)[/tex]          use the distributive property[tex]y+1=\dfrac{1}{3}x+\dfrac{2}{3}[/tex]           subtract 1 = 3/3 from both sides[tex]y=\dfrac{1}{3}x-\dfrac{1}{3}[/tex]