Rosetta wants to write equations in the form y=mx+b for the lines passing through point p that are parallel and perpendicular to line g. first she finds the slopes of these two lines. what could she do next to find the y-intercepts?

a. substitute the slope and the coordinates of point p in y=mx+b and then solve for b for each equation.
b. multiply the slope by the x-coordinate and add the y-coordinate to the product.
c. multiply the slope by the y-coordinate and subtract the result from the x-coordinate.
d. solve the proportion m/b=y/x for b.

A. Substitute the slope and the coordinates of point P in y=mx+b and then solve for b for each equation.

Step-by-step explanation:

We know the equation for a line passing through a point P(x,y) is given as:

y = mx + b

where

m is the slope of the line.

x, y are the co-ordinates of point P.

b is the y-intercept of line on point P(x,y).

If g is the line. we find its slop m. Let's the slope 'm' is given as m = b/a

The slope of lines parallel to line g is b/a.

The slope of lines perpendicular to line g is -a/b.

Substituting the slope and and coordinates of point P and then solving for b will give us the y-intercept.

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b