Question

HURRY I'LL PICK A BRAINLIEST PERSON!!!

Answer 1

Step 1

Find the slope of the line PQ

we know that

the formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$P(-3,-3)\\Q(3,-1)$

substitute the values

$m=\frac{-1+3}{3+3}$

$m=\frac{2}{6}$

$m=\frac{1}{3}$

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

$y-y1=m(x-x1)$

we have

$m=\frac{1}{3}$

$(x1,y1)=R(1,1)$

substitute the values

$y-1=\frac{1}{3}(x-1)$

Step 3

we know that

The point on the y-axis that is on the line $y-1=\frac{1}{3}(x-1)$ 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 $x=0$ find the value of y in the linear equation

$y-1=\frac{1}{3}(0-1)$

$y-1=-\frac{1}{3}$

$y=1-\frac{1}{3}$

$y=\frac{2}{3}$

The point that is on the y-axis is $(0,\frac{2}{3})$

therefore

the answer is the option A

$(0,\frac{2}{3})$

see the attached figure to better understand the problem

Answer 2

Answer: A.(0,2/3 )

Step-by-step explanation:

Let A (0,y) be the point on y axis is on the line that passes through point R (1,1) and is parallel to line PQ.

We know that if two lines are parallel then their slopes are equal.

The slope of line passing through  (a,b) and (c,d) is given by

$m=\frac{d-b}{c-a}$

Since AR is parallel to PQ.

Then slope of PQ= slope of AR

$\frac{-1-(-3)}{3-(-3)}=\frac{1-y}{1-0}\\\Rightarrow\frac{2}{6}=\frac{1-y}{1}\\\\\Rightarrow\frac{1}{3}=1-y\\\Rightarrow\ y=1-\frac{1}{3}\\\Rightarrow\ y=\frac{2}{3}$

hence, the point on the y-axis is on the line that passes through point R and is parallel to line PQ = (2/3,0)