Answer:
To find an equation of the line that passes through the point (-2, -3) and is parallel to the line 4x-y = 1, we know that the slope of the line we are looking for must be the same as the slope of the line 4x-y = 1. We can find the slope of 4x-y = 1 by rearranging it to the slope-intercept form y = mx + b.
4x - y = 1
y = -4x + 1
The slope of this line is -4
Now that we know the slope of the line we are looking for is -4, we can use the point-slope form of a linear equation, which is:
y - y1 = m (x - x1)
where (x1, y1) is a point on the line, and m is the slope.
We know that the point (-2, -3) is on the line we are looking for, so we can substitute these values into the point-slope form:
y - (-3) = -4 (x - (-2))
y + 3 = -4x + 8
y = -4x + 5
So an equation of the line that passes through the point (-2, -3) and is parallel to the line 4x-y = 1 is y = -4x + 5.