Find an equation of the line passing through the point ( 6 , − 4 ) (6,-4) and perpendicular to 9 x − 3 y = 9 9x-3y=9 . write your answer in slope-intercept form.

Step-by-step explanation:

We are given;

A point (6, -4)An equation of a line, 9x - 3y = 9

We are required to determine the equation a line passing through a point (6, -4) and perpendicular to the given line;

To answer the question we need to get the gradient of the given line first.We write the equation 9x - 3y = 9  in the form of y = mx + c, where m is the slope;That is;

y = 3x -3

Thus, the slope of the line is 3

But; m₁ × m₂ = -1 (For perpendicular lines)

Therefore;

m₂ = -1 ÷ 3

    = -1/3

Therefore, the slope of the line in question is -1/3 and the line passes through (6, -4).

To get its equation, we get another point (x, y)

Then;

Thus;

In the form of slope-intercept, the equation will be;

Thus, the equation of the line is;

Unitary pencil cost= $2.06

Step-by-step explanation:

Giving the following information:

Total cost= $22.35

Pad cost= $9.99

Number of pencils= 6

First, we need to calculate the total cost spend on pencils.

Total pencils cost= total cost - pad cost

Total pencils cost= 22.35 - 9.99

Total pencils cost= $12.36

Now, the cost of each pencil:

Unitary pencil cost= 12.36/6

Unitary pencil cost= $2.06