Question

How do you write the equation `y-5=6(x+1)` in slope intercept form?

Answer 1

See a solution process below:

Explanation:

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.

First, expand the terms in parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`y - 5 = color(red)(6)(x + 1)`

`y - 5 = (color(red)(6) xx x) + (color(red)(6) xx 1)`

`y - 5 = 6x + 6`

Now, add `color(red)(5)` to each side of the equation to solve for `y` while keeping the equation balanced:

`y - 5 + color(red)(5) = 6x + 6 + color(red)(5)`

`y - 0 = 6x + 11`

`y = color(red)(6)x + color(blue)(11)`