Question

Point and slope. slope =-(1)/(4) through (4,-3)

Answer 1

The equation of the line in point-slope form, given that the slope of the line is
`-(1)/(4)`, is:

• 4y + 12 = 4 - x

How to determine the equation of the line in the point-slope form?

In point-slope form as regarding the equation of the line, the x variable is on one side, while the y variable is on the other side

Now, we were given the following from the question:

• Slope of line (m) =
  `-(1)/(4)`
• Coordinate of line = (4, -3)
• x coordinate of line (x₁) = 4
• y coordinate of line (y₁) = -3
• Equation in point slope form =?

`y\ -\ y_1 = m(x\ -\ x_1)\\\\y\ -\ (-3) = -(1)/(4) (x\ -\ 4)\\\\y\ +\ 3 = (-x\ +\ 4)/(4)\\\\Cross\ multiply\\\\4(y\ +\ 3) = -x\ +\ 4\\\\4y\ +\ 12 = -x\ +\ 4\\\\Rearrange \\\\4y\ +\ 12 = 4\ -\ x`

Therefore, the equation in point-slope format is: 4y + 12 = 4 - x

Complete question:

What is the point and slope equation of a line having slope =-(1)/(4) through point (4,-3)?