Question

Find an equation of the line with the given slope that passes through the given point. Write the equation in the form Ax + By = C.

m = 4, (6,6)

Answer 1

`4x-y=18`

Explanation:

We want to find the equation of a line in standard form with a slope of 4 and passes through the point (6, 6).

First, we can write it in point-slope form. Point-slope form is given by:

`y-y_1=m\left(x-x_1\right)`

Where (x₁, y₁) is a point and m is the slope.

Substitute:

`y-6=4(x-6)`

Distribute the right:

`y-6=4x-24`

Now, we can separate all the variables and the constants. Subtract 4x from both sides:

`-4x+y-6=-24`

Add add 6 to both sides:

`-4x+y=-18`

Traditionally, A or the coefficient of x is always positive. Hence, we can divide both sides by -1 to acquire:

`4x-y=18`