Answer:
Option: B is the correct answer.
B. Plot the point (0, -1), move up 2 and right 3, plot the point, and draw the line through these 2 points.
Step-by-step explanation:
The equation of a line is given by:
[tex]y=\dfrac{2}{3}x-1[/tex]
A)
Plot the point (0, -1), move up 3 and right 2, plot the point, and draw the line through these 2 points.
Now when we move up 3 units and 2 units to the right then the point is: (2,2)
This means that the graph of the function must pass through (2,2)
when x=2 then the value from the actual function is:
[tex]y=\dfrac{2}{3}\times 2-1\\\\\\y=\dfrac{4-3}{3}\\\\\\y=\dfrac{1}{3}\neq 2[/tex]
Hence, option: A is incorrect.
C)
Plot the point (-1, 0), move up 2 and right 3, plot the point, and draw the line through these 2 points.
This means that the equation of the line must pass through (-1,0) and (2,2)
Now when x= -1 we have:
[tex]y=\dfrac{2}{3}\times (-1)-1\\\\\\y=\dfrac{-2-3}{3}\\\\\\y=\dfrac{-5}{3}\neq 0[/tex]
Hence, option: C is incorrect.
B)
Plot the point (0, -1), move up 2 and right 3, plot the point, and draw the line through these 2 points.
i.e. the line must pass through (0,-1) and (3,1)
Now we find the equation of a line using the two points as:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
where (a,b) and (c,d) are the passing through points.
Here (a,b)=(0,-1) and (c,d)=(3,1)
Hence, we have the equation of line as:
[tex]y-(-1)=\dfrac{1-(-1)}{3-0}\times (x-0)\\\\\\y+1=\dfrac{2}{3}x\\\\\\y=\dfrac{2}{3}x-1[/tex]
Hence, it matches the actual equation of the line.
Hence, option: B is the correct answer.
