Write the equation of the line (5,7);x+5y=4

Answer 1

x+5y=4 is the equation of a line, but it doesn't pass through the point (5,7)

plug x=5 and y=7 into the equation, and you get 5+5(7) = 4 or 40=4

maybe you left out a 0? and you meant 40 instead of 4?

Or sometimes the problem gives you one equation and asks for a new equation that is parallel or perpendicular to the given equation that passes through a point

Put x+5y=4 in y=mx+b form to find the slope.

5y=-x+4

y = x/5 +4/5 It has slope = 1/5, the coefficient of the x term

A line parallel will have the same slope = 1/5.

A line perpendicular will have a slope that is the negative inverse of 1/5 or -5

For the parallel equation going through (5,7), it's y=x/5 + b plug in x=5, y=7 to get b

7=5/5 + b

7=1+b

b=6

The equation of a line parallel going through (5,7) is y=x/5 + 6

or in integral form: 5y =x +30

For the equation of a line perpendicular, y=-5x+b

7=-25+b

b=32

y=-5x+32 is the equation of a line perpendicular passing through (5,7)