We have to find the equation of the line.
To find the equation, we only need two points that belong to the line.
We can pick the points (0,-1) and (6,3) and calculate the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-1)}{6-0}=\frac{4}{6}=\frac{2}{3}[/tex]
The point (0,-1) gives us the y-intercept b = -1, so we can write the equation of the line as:
[tex]y=\frac{2}{3}x-1[/tex]
We have to find the coordinates for the point (a,b).
We have infinite possibilities for a, and then b is found using the equation of the line.
We can see that a, the x-coordinate, correspond to x = 3, so a = 3.
Then, we can calculate b using the equation of the line:
[tex]b=y(a)=y(3)=\frac{2}{3}(3)-1=2-1=1[/tex]
Then, we have (a,b) = (3,1).
The y-coordinate when x = 0 is y = -1, as we know the point (0, -1) that belongs to the line.
Answer:
The slope of the line is m = 2/3.
The equation of the line is y = 2/3*x -1
The values of a and b are a = 3 and b = 1.
When x = 0, the y-coordinate is y = -1.
