Answer:
B. [tex]y-9=2(x-1)[/tex]
Step-by-step explanation:
We have been given graph of a line on coordinate plane. We are asked to find the equation of our given line.
First of all, we will find slope of our line using points [tex](-2,3)\text{ and }(1,9)[/tex] in slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{9-3}{1-(-2)}[/tex]
[tex]m=\frac{6}{1+2}[/tex]
[tex]m=\frac{6}{3}[/tex]
[tex]m=2[/tex]
We can see that our given equations are in point-slope form of equation: [tex](y-y_1)=m(x-x_1)[/tex], where,
m = Slope,
[tex](x_1,y_1)[/tex] = Coordinates of point on line.
We can get two equations of our line in point-slope form as:
[tex](y-3)=2(x--2)[/tex]
[tex](y-3)=2(x+2)[/tex] or
[tex](y-9)=2(x-1)[/tex]
Upon looking at our given choices, we can see that option B is the correct choice.
