Answer:
B. [tex]y-1=\frac{2}{3}(x-3)[/tex]
Step-by-step explanation:
We have been given an image of a line on coordinate plane. We are asked to find the equation of our given line in point-slope form.
We know that point-slope form of equation is in format: [tex](y-y_1)=m(x-x_1)[/tex], where,
m = Slope of line,
[tex](x_1,y_1)[/tex] = Coordinates of the point on line.
First of all, we will find slope of our given line using the coordinates of points [tex](-3,-3)[/tex] and [tex](3,1)[/tex] in slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{1--3}{3--3}[/tex]
[tex]m=\frac{1+3}{3+3}[/tex]
[tex]m=\frac{4}{6}[/tex]
[tex]m=\frac{2}{3}[/tex]
Upon substituting [tex]m=\frac{2}{3}[/tex] and coordinates of point [tex](3,1)[/tex] in point-slope form of equation, we will get:
[tex](y-1)=\frac{2}{3}(x-3)[/tex]
[tex]y-1=\frac{2}{3}(x-3)[/tex]
Therefore, option B is the correct choice.
