Question

What is the slope intercept form of the line with a slope of `-2/5` and y-intercept of `-4/7`?

Answer 1

Simple: `y=-2/5x-4/7`.

Explanation:

Slope-intercept form `(y=mx+b)` is called that because those two pieces of information (the slope `m` and the `y`-intercept `b`) are seen directly in the formula.

Since we are given the value for slope as `m=-2/5` and the value for the `y`-intercept as `b=-4/7`, we simply plug these two values into the raw formula and simplify to arrive at

`y="      "m"     "x+"       "b`

`y=(-2/5)x+(-4/7)`

`y=-2/5x-4/7.`

The slope tells you how fast `y` changes relative to `x` (in this case, `-2/5` times as fast), and the `y`-intercept tells you the value of `y` when `x=0.` If you plug `x=0` into the equation, you get

`y=-2/5(0)-4/7`

`color(white)y=-4/7.`