find an equation in the form of y=mx+b. Through (3, -5), parallel to y=4

Use the formula:

\frac{y\ -\ y-coordinate}{x\ -\ x-coordinate} = m

For example, if you had (2, 1) with gradient 1,

\frac{y - 1}{x-2} = 1

This gives:

y-1 = x - 2

y = x -1

which is in the form y = mx + c.

EDIT: Note that a line parallel to the x-axis has a gradient of 0, and that parallel to the y-axis has gradient infinity.

Post your answer! :)

The general form of the linear equation has two parameters: m and b. So you need two unrelated pieces of information to calculate them. Those are the parallel line and the given point.

1. the parallel line:
y = 4 can be rewritten as y = 0 * x + 4
parallel means: having the same m value. So read the m value from the above equation and replace m in the result equation with that value.

2. the given point
Next replace x and y with the respective values from the given point and resolve to b. Now you have m and b and can give the result equation.