What is the equation, in slope-intercept form, of the line that is perpendicular to the line
y – 4 = –two-thirds(x – 6) and passes through the point (−2, −2)?

Step-by-step explanation:

We are given;

The equation of a line;

We are required to determine the equation of a line perpendicular to the above line and passing through (-2, -2).

We need to know that the product of gradient of two parallel lines is -1

m₁× m₂ = -1

Thus;

m₂ = -1 ÷ -2/3

     = 3/2

Thus, the gradient is 3/2 and the line passes through (-2,-2)

Thus, to get its equation, we take another point (x,y)

We get;

Then;

Combining the like terms,

In the form of slope-intercept;

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w