Answer:
Yes, he is correct because both the lines have same slope.
Step-by-step explanation:
Given:
The two equations are:
[tex]-2x+6y=-42\\y+10=\frac{1}{3}(x-3)[/tex]
Two lines are parallel only if their slopes are equal.
So, let us write each equation in slope-intercept form [tex]y=mx + b[/tex], where, [tex]m[/tex] is the slope of the line.
Equation 1 is:
[tex]-2x+6y=-42\\6y=2x-42\\y=\frac{2}{6}x-\frac{42}{6}\\y=\frac{1}{3}x-7[/tex]
So, the slope of line 1 is [tex]m_{1}=\frac{1}{3}[/tex]
Now, equation 2 is:
[tex]y+10=\frac{1}{3}(x-3)\\y+10=\frac{1}{3}x-3\times \frac{1}{3}\\y+10=\frac{1}{3}x-1\\y=\frac{1}{3}x-1-10\\y=\frac{1}{3}x-11[/tex]
Therefore, slope of line 2 is, [tex]m_{2}=\frac{1}{3}[/tex]
∵ [tex]m_{1}=m_{2}=\frac{1}{3}[/tex]
Therefore, both the lines are parallel to each other.
