Answer:
y = 6x + 1
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