Question

What is the slope intercept form of the line passing through `(-4,7)` with a slope of `-1/3`?

Answer 1

See the entire 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 and values for the point from the problem for `m`, `x` and `y` in the formula and solve for `b`:

`7 = (color(red)(-1/3) * -4) + color(blue)(b)`

`7 = 4/3 + color(blue)(b)`

`7 - color(red)(4/3) = 4/3 - color(red)(4/3) + color(blue)(b)`

`(3/3 * 7) - color(red)(4/3) = 0 + color(blue)(b)`

`21/3 - color(red)(4/3) = color(blue)(b)`

`17/3 = color(blue)(b)`

We can now substitute the slope given in the problem and the value for `b` we calculated into the slope-intercept formula to find the equation to solve the problem:

`y = color(red)(-1/3)x + color(blue)(17/3)`