Question

which is the equation of the line that is parallel to the given line and passes through the point (-2,2)

Answer 1

So first you want to find the slope of the blue line.

To do this you can use the slope formula:

m = (
`y_(2) - y_(1)`) / ([tex] x_{2} - x_{1})

So take two points, which are already listed here.

(-5, -4) and (0, -3)

So if you input the numbers into the equation, you get:

(-4 - (-3))/(-5 - 0)

(-1) / (-5)

1/5 is the slope.

So therefore you know two key parts of the equation of the line parallel to the blue line: the slope (since they're parallel and never meet) and also a point on that line.

y = mx + b is the basic equation of a line, with m being the slope and b being the y intercept. We want to fill these in.

So we already know the slope.

So what we have in the equation right now is:

y = 1/5x + b

Since we have a point already, we can fill in that point for y and x to solve for b.

(-2, 2) is the point.

So filling it in, you get:

2 = 1/5(-2) + b

2 = -2/5 + b

b = 12/5

And then you have the equation, or:

y = 1/5x + 12/5