6x + y = 28. The standard form of the equation that is parallel to y = -6x + 5 and goes through point (4, 4) is 6x + y = 28.
The equation is written in the slope-intercept form y = mx +b. So:
y = -6x + 5
The slope m = -6
Since the slopes of parallel lines are the same, we are looking for a slope line m = -6 and goes through point (4, 4).
With the slope-intercept form:
y = mx + b
Introducing the slope m = -6:
y = -6x + b
Introducing the point (4, 4):
4 = -6(4) + b
b = 4 + 6(4)
b= 24 + 4
b = 28
Then
y = -6x + 28
write the equation in standard form ax + by = c:
y = -6x + 28
6x + y = 28