Question 257351
i need to write an equation of the line containing the given point and parallel to given line i do not understand how to express in y=mx+b.
(2,9,); x+4y=9 

We need to rewrite the equation x + 4y = 9  in slope-intercept form:

x + 4y = 9
4y = -x - 9
y = (-1/4)*x - 9/4.

So from this we know that the slope of the line is -1/4. A line parallel to this line will also have a slope of -1/4.

So the equation of the parallel line is:

y = (-1/4)*x + b.

We need to find b. Since the point (2,9) is on our line we know:

9 = (-1/4)*2 + b 
b = 9.5

The equation of the parallel line then is y = (-1/4)*x + 9.5