Question

What is the slope intercept form of the line passing through `(1,11)` with a slope of `-13`?

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.

We can substitute the slope given in the problem for `color(red)(m)` and the values of the point given in the problem for `x` and `y` and solve for `color(blue)(b)`

`11 = (color(red)(-13) xx 1) + color(blue)(b)`

`11 = -13 + color(blue)(b)`

`color(red)(13) + 11 = color(red)(13) - 13 + color(blue)(b)`

`24 = 0 + color(blue)(b)`

`24 = color(blue)(b)`

`color(blue)(b) = 24`

We can now substitute the slope from the problem and the value of `b` we calculated to write the equation:

`y = color(red)(-13)x + color(blue)(24)`