Question

Write and equation of a line that is parallel to the line below and passes through the given point

Answer 1

If one line is parallel to another, that means the two lines have the same slope. Therefore, since the line you are creating is parallel to the line y = -2/3x - 5, it's slope must be the same, -2/3. Additionally, you know it passes through the point (-3, 11).

If you don't remember the slope-intercept equation, it looks like this:
y = mx + b, where m is the slope, b is the y-intercept, and x and y are, well, x and y.

Let's plug in the slope we know it must have (-2/3) and plug in the (x, y) coordinates we were provided so that we can find b.
11 = -2/3(-3) + b

Solve for b:
11 = 2 + b
9 = b

Now we know our slope and our y-intercept, after solving for it, so we can write our final equation!

The answer is: y = -2/3x + 9

Answer 2

a line parrelel would have the same slope

in y=mx+b m=slope and b=yintercept

so y=-2/3x-5
the point you want is -3,11 or this equation is true when x=-3 and y=11 are true so subsitute and solve for the new 'b'

11=-2/3(-3)+b
11=2+b
subtract 2 from both sides
9=b

the equaqtion is y=-2/3x+9