A parallel line means our new line will have a slope equal to the original line.
The original line is in slope-intercept form, y = mx + b, where m is the slope and b is the value of the y-intercept. This tells us that the slope we want to use is m = -3
By using a slope of -3, with the given point (3,-4), we can now use the point-slope formula to find our new line.
Point-slope formula: y - y1 = m(x - x1) where m is the slope and the line passes through the point (x1,y1)
Combining our point and slope, we get:
y + 4 = -3(x - 3)
If we wish, we can rearrange this by distributing on the right hand side.
y + 4 = -3x + 9
We can then subtract 4 from both sides to get our answer in slope-intercept form
y + 4 - 4 = -3x + 9 - 4
y = -3x + 5