Question

How do you write the equation of a line in point slope form and slope intercept form given point (6, -3) and has a slope of 1/2?

Answer 1

Point-Slope Form is
`y+3 = 1/2(x-6)`

Slope-Intercept Form is
`y = 1/2x-6`

Explanation:

The point-slope form of the equation of a line is

`y-y_1 = m(x-x_1)`

Where `m` is the slope and the point is `(x_1,y_1)`

For this problem

`m=1/2`
`x_1 = 6`
`y_1=-3`

Plug in the values

`y-(-3) = 1/2(x-6)`

Simplify the signs

`y+3 = 1/2(x-6)`
This is the point-slope form of the equation

Now solve for `y` to get the slope-intercept form.

`y+3 = 1/2(x-6)`

Use the distributive property to eliminate the parenthesis

`y+3 = 1/2x-3`

Now isolate the `y` using the additive inverse

`y cancel(+3) cancel(-3) = 1/2x-3-3`

`y = 1/2x-6`
This is the slope-intercept form of the equation

Answer 2

See a solution process below:

Explanation:

The point-slope form of a linear equation is:

`(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))`

Where `(color(blue)(x_1), color(blue)(y_1))` is a point on the line and `color(red)(m)` is the slope

Substituting the slope and values from the point in the problem gives:

`(y - color(blue)(-3)) = color(red)(1/2)(x - color(blue)(6))`

`(y + color(blue)(3)) = color(red)(1/2)(x - color(blue)(6))`

The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

We can solve the point-slope equation for `y` giving:

`(y + color(blue)(3)) = color(red)(1/2)(x - color(blue)(6))`

`y + color(blue)(3) = (color(red)(1/2) xx x) - (color(red)(1/2) xx color(blue)(6))`

`y + color(blue)(3) = 1/2x - 6/2`

`y + color(blue)(3) = 1/2x - 3`

`y + color(blue)(3) - color(blue)(3) = 1/2x - 3 - color(blue)(3)`

`y + 0 = 1/2x - 6`

`y = color(red)(1/2)x - color(blue)(6)`