Question

Write an equation in point-slope form of the line that passes through the point (5,6) with slope 3/5

Answer 1

`\boxed{y - 6 = (3)/(5) (x - 5)}`

Explanation:

Given:

• Line passes through: (5,6)
• Slope = 3/5 = 0.6

Formula:

• 
  `y - y_(1) = m(x - x_(1) ) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{m = Slope}; \ (x_1},y_(1)) = \text{Coordinates of point}]`

Substitute the values into point slope form to determine the equation of the line in point slope form.

`\implies y - y_(1) = m(x - x_(1) )`

`\implies \boxed{y - 6 = (3)/(5) (x - 5)}`

Answer 2

point-slope form:

• y - y₁ = m(x-x₁)

slope intercept form:

• y = mx + b

Equation:

`\sf \hookrightarrow y-6 = (3)/(5) (x-5)`
`\sf [ \ this \ is \ point \ slope \ form \ equation \ ]`

`\sf \hookrightarrow y-6 = (3)/(5) x-3` ----------------

`\sf \hookrightarrow y= (3)/(5) x-3+6` -------------------

`\sf \hookrightarrow y= (3)/(5) x+3`
`\sf [ \ this \ is \ slope \ intercept \ form \ equation \ ]`