Question

what type of line is the graph of 4x+y=-3

Answer 1

You'll have to provide a better question. It's a line. What sort of characteristics are we to identify? Maybe put it in slope-intercept form and identify those items?

Answer 2

Falling (leaning to the left).

If you transform it to its slope-intercept form, y = mx + b, the equation will look like:

y = -4x - 3

Now, the slope of the line (represented by m in the slope-intercept form), tells you whether the line is vertical, horizontal, rising (leaning to the right), and falling.

A line is vertical if the slope is UNDEFINED. This can be seen if the line's equation is only characterized by x = a.

A line is horizontal if the slope is 0. This can be seen if the line's equation is only characterized by y = b.

A line is rising if the slope is POSITIVE.

A line is falling if the slope is NEGATIVE

In your case, the slope m is negative (as it is equal to -4, the coefficient of x). Thus, your line is falling.