The general form of the equation of a line is represented by the Affine function y = mx + b, in which m represents the slope, b the y-intercept, y and x the coordinates of a point.
By hypothesis, we got the slope (m = 4), and the coordinates of a point (in which x = 0 and y = -9). So all we need to do is to find the y-intercept b.
Let's replace the values we have in the equation y = mx + b:

-9 = 4*0 + b
-9 = 0 + b
-9 = b.

We got now the y-intercept. So the final equation of the line is:
y = 4x - 9

If we subtract 4x from each side, we get:
y - 4x = -9
And if we multiply both sides by -1, we get:
4x - y = 9

So the equation of the line, based on your choices, is 4x - y = 9.

I've added a picture of the graph of the equation under the answer.

Hope this Helps! :)

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4 years ago