Answer:
The equation of the parallel line is:
[tex]y=-\frac{1}{3} x+\frac{34}{3}[/tex]
Step-by-step explanation:
First express the given line in slope-intercept form:
[tex]x+3\,y = 7\\3\,y = -x+7\\y=-\frac{1}{3} x+\frac{7}{3}[/tex]
Since we want a line parallel to this, the new line must have the same slope (-1/3). We add to that the condition of the line going through the point (7, 9):
[tex]y=-\frac{1}{3} x+b\\9=-\frac{1}{3} (7)+b\\9=-\frac{7}{3} +b\\b=9+\frac{7}{3} \\b=\frac{34}{3}[/tex]
Therefore,the equation of the parallel line is:
[tex]y=-\frac{1}{3} x+\frac{34}{3}[/tex]
