Question

Linear equation

A line with the slope of 1/2 pass through the point (3,-2)
a) Write the equation of the line in Point - Slope Form.
b) Write the equation of the line in Slope - intercept form.

Answer 1

see explanation

Explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m =
`(1)/(2)` and (a, b) = (3, - 2) , thus

y - (- 2) =
`(1)/(2)` (x - 3) , that is

y + 2 =
`(1)/(2)`( x - 3) ← in point- slope form

(b)

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m =
`(1)/(2)` , thus

y =
`(1)/(2)` x + c ← is the partial equation

To find c substitute (3, - 2) into the partial equation

- 2 =
`(3)/(2)` + c ⇒ c = - 2 -
`(3)/(2)` = -
`(7)/(2)`

y =
`(1)/(2)` x -
`(7)/(2)` ← in slope- intercept form