Question

Question #76df0

Answer 1

The equation would be `y = mx + b`

Explanation:

B is the y intercept, the point of the line that touches some part of the y-axis.

M is the slope (rise over run). You find it by plugging two points on the line into the slope equation: `m = (y_2 - y_1)/(X_2 - x_1)`.

Y is basically the linear function.

So if I have a line with the equation: `y = 2x + 1`

I can plug in values for `x` and `y` (let's say 1). I replace `x` with 1 so --> `y = 2(1) + 1`. SO if `x` is 1, then I can solve the equation and say `y = 3`. That's one point (1, 3) on the line of the equation above. Another value to find another point. `b` is 1 because `y` = 2`x` + 1. That means at (x, `1`) the line touches the y-axis.

And as I gave the equations above, when you find the second coordinate (the first being (1, 3)) by plugging in another value for `x` and solving for `y`, you can find `m`, the slope.

Answer 2

Perhaps the question refers to the "intercept form" of a line:

`x/a +y/b=1`,
where the `x` intercept is `(a,0)` and the `y` intercept is `(0,b)`.

To convert this form to slope intercept form `y=mx+b` (where `m` is the slope and `b` is the `y` intercept),

multiply the equation `x/a +y/b=1` by the LCD `ab`

`ab(x/a +y/b =1)`

`(abx)/a +(aby)/b=ab`

`bx+ay=ab`
`-bxcolor(white)(aaa)-bx`

`ay=-bx+ab`

`(ay)/a=(-bx)/a+(ab)/a`

`y=(-b/a)x +b`

So, to convert from the "intercept form" of a line `x/a+y/b=1`
to the "slope intercept form" `y=mx+b`,

the slope `m=-b/a` and the y intercept `b` is equal to the "b" in the intercept form.