Question

How do you write an equation in standard form for a line passing through (2, -3), m= -3.6?

Answer 1

`18x + 5y = 21`

Explanation:

The standard form of a linear equation is `Ax + By = C`.

Since we are given a slope and a point, the slope-intercept form of a linear equation will quickly provide us with an answer.

Recall that any (non-vertical) line can be written in the form `y = mx + b`, where `m` is our slope and `b` is our initial value. We find `b` by plugging in the provided point and slope:

`y = mx + b`
`y = -3.6x + b`
`-3 = -3.6(2) + b`
`-3 = -7.2 + b`
`4.2 = b`

Thus, our linear equation in slope-intercept form is `y = -3.6x + 4.2`. By moving our term containing `x` to the left-hand side of the equation, we obtain our equation in standard form:

`y = -3.6x + 4.2`
`3.6x + y = 4.2`

We can clean up our answer by multiplying through by `10` to remove our decimals, then simplifying.

`3.6x + y = 4.2`
`36x + 10y = 42`
`18x + 5y = 21`