Answer: y = -(3/7)x - (36/7)
Step-by-step explanation:
Let's convert -3x - 7y = 10 to standard slope intercept form: y=mx + b, where m is the slope and b is the y-intercept (the value of y when x=0).
-3x - 7y = 10
-7y = 3x + 10
y = -(3/7)x - (10/7)
This line has a slope of -(3/7). Any line that is parallel will have the same slope, so we can write y = -(3/7)x + b to start our new line.
We want a value of b that forces the line to go trough point (-5,-3). Use this point in the partial equation and solve for b:
y = -(3/7)x + b
-3 = -(3/7)(-5) + b
-3 = (15/7) + b
b = -3 - (15/7)
b = -(21/7) - (15/7)
b = -(36/7), or -5 1/7
y = -(3/7)x - (36/7)
