Step 1
Find the slope of the line PQ
we know that
the formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]P(-3,-3)\\Q(3,-1)[/tex]
substitute the values
[tex]m=\frac{-1+3}{3+3}[/tex]
[tex]m=\frac{2}{6}[/tex]
[tex]m=\frac{1}{3}[/tex]
Step 2
Find the equation of the line that passes through point R ans is parallel to line PQ
we know that
If two lines are parallel, then their slopes are the same
The equation of the line into point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{1}{3}[/tex]
[tex](x1,y1)=R(1,1)[/tex]
substitute the values
[tex]y-1=\frac{1}{3}(x-1)[/tex]
Step 3
we know that
The point on the y-axis that is on the line [tex]y-1=\frac{1}{3}(x-1)[/tex] is equal to the y-intercept of the line
The y-intercept is the value of y when the value of x is equal to zero
so
For [tex]x=0[/tex] find the value of y in the linear equation
[tex]y-1=\frac{1}{3}(0-1)[/tex]
[tex]y-1=-\frac{1}{3}[/tex]
[tex]y=1-\frac{1}{3}[/tex]
[tex]y=\frac{2}{3}[/tex]
The point that is on the y-axis is [tex](0,\frac{2}{3})[/tex]
therefore
the answer is the option A
[tex](0,\frac{2}{3})[/tex]
see the attached figure to better understand the problem
