Write the equation of the line that satisfies the given conditions. Express the final equation in standard form. Contains the point (-2, 1) and is perpendicular to the line 5x − y = 4

Answer 1

The given line 5x - y = 4

5x - y - 4 = 0

5x - 4 = y

the given line has slope 5.

The perpendicular line has slope m= (-1/5)

It eats (-2,1) --> x=-2 when y=1

B = y - mx = 1- (-1/5)(-2) = 1 - (2/5) = 3/5

y = (-1/5)x + 3/5

Standard Form:

5y = -x + 3

x + 5y = 3

Answer 2

First to make things easier, we can rewrite

5x - y = 4 to y = 5x - 4.

the problem tells us that the lines are perpendicular so we know that the slopes must be negative reciprocals of each other ( x, -1/x). The negative reciprocal of 5 ( slope of given line) is -1/5, so we know that our new line follows the format y = -1/5 X + b, now we must solve for the why intercept that would allow our line to pass through the point, (-2,1) plug -2 for x and 1 for y to get

1 = (-1/5)*-2 + b

1 = 2/5 + b

3/5 = b

therefore the equation of the line is

Y = -1/5 X + 3/5