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
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