Write an equation of the line containing the given point and perpendicular to the given line. express your answer in the form y=mx+b. (3,7); 7x+y=4. simplify

Let's first solve 7x+y=4 for y

Subtract 7x from both sides to accomplish this

7x+y=4
7x+y-7x=4-7x
y = -7x+4

This equation has a slope of -7. This is the same as -7/1

Flip the fraction to get -1/7 and then flip the sign from negative to positive to get +1/7 = 1/7

The slope of this unknown perpendicular line is going to be m = 1/7

We now use the point (3,7) to figure out the value of b

y = mx + b
y = (1/7)*x + b ... plug in the value of m found earlier
7 = (1/7)*3 + b ... plug in the given point; solve for b
7 = (3/7) + b
7-(3/7) = b
49/7 - 3/7 = b
b = 46/7

So the answer in y = mx+b form is
y = (1/7)x + 46/7
where
m = 1/7 is the slope
b = 46/7 is the y intercept