What is an equation of the line that passes through the point (1,7) and is perpendicular to the line x+6y=42

y = 6x + 1

Step-by-step explanation:

We are asked to find the equation of the line that is perpendicular to x + 6y = 42

Step 1: find the slope

x + 6y = 42

6y = 42 - x

Divide both sides by 6, to make y the subject of the formula

6y/6 = (42 - x) /6

y = (42 - x) /6

Following the equation of a line

y = mx + c

We can separate and rearrange

y = 42/6 - x /6

y = -x/6 + 42/6

y = -x/6 + 7

Slope m = -1/6

Note: if two lines are perpendicular to the other, they are negative reciprocal of each other

ie m is the negative reciprocal of -1/6

m = 6/1 or 6

Step 2: using the formula for point slope form

y - y_1 = m(x - x_1 )

m = 6

Point ( 1 ,7)

x_1 = 1

y_1 = 7

y - 7 = 6(x - 1)

Open the bracket

y - 7 = 6x - 6

Step 3: using a slope intercept form

y = mx + c

y - 7 = 6x - 6

y = 6x - 6 + 7

y = 6x + 1

The equation of the line is

y = 6x + 1