Answer:
[tex]y=-\frac{5}{3} x+4[/tex]
Step-by-step explanation:
Since the line we are trying to study is parallel to the one given by the standard equation 5x + 3y = 6, it needs to have the same slope as this given line has. Let's write then this equation in slope-intercept so we can find what the slope is :
[tex]5x+3y=6\\3y=-5x+6\\y=-\frac{5}{3} x+\frac{6}{3} \\y=-\frac{5}{3} x+2[/tex]
Then the slope of our line must also be "-5/3" in order to be parallel to the given line.
Now, since we also know a point (3, -1) through which the new line should go, we use the point-slope form of a line:
[tex]y-y_0=m(x-x_0)\\y-(-1)=-\frac{5}{3} (x-3)\\y+1=-\frac{5}{3} x+5\\y=-\frac{5}{3} x+4[/tex]
