Answer:
[tex]y=-4\,x-4[/tex] which agrees with answer "A" in the list of possible options
Step-by-step explanation:
From the fact that there is a steady rate of increase in the x and in the respective y values (notice that x increases in steps of 1 unit, and at the same time y values increase in steps of "-4" units) the data belongs to the equation of a line.
We can determine that equation using just two pairs of points, like for example (-1, 0) and (0, -4).
We first find the slope using the slope formula for the segment that joints any two points on the plane:
[tex]slope=\frac{y_2-y_1}{x_2-x_1} \\slope=\frac{-4-0}{0-(-1)}\\slope = -4[/tex]
we now write the slope-intercept general form of a line with slope "-4", and solve for the intercept by using the point (0,-4) which should be in the line:
[tex]y=m\.x+b\\y=-4\,x+b\\-4=-4\,(0)+b\\b=-4[/tex]
Therefore the equation for this points is:
[tex]y=-4\,x-4[/tex]
