Question

How do you write an equation in standard form of the lines passing through (-1,5) and (0,8)?

Answer 1

`3x-y = -8`

Explanation:

Start with a two point form (based on slope)
`color(white)("XXXX")` `(y-8)/(x-0) = (8-5)/(0-(-1)`
Which simplifies as
`color(white)("XXXX")` `y-8 = 3x`

Standard form of a linear equation is
`color(white)("XXXX")` `Ax+By=C` with `A, B, C epsilon ZZ` and `A>=0`

Converting `y-8 = 3x` into this form:
`color(white)("XXXX")` `3x-y = -8`

Answer 2

`-3x+y=8`

Explanation:

The standard form of an equation is given by;
`Ax+By=C`

To find the equation of line passing through the points (-1,5) and (0,8), we need to used given formula;

`(y-y_1)=m(x-x_1)`..........equation 1
where m = slope and given by the formula;

`m=\frac{y_2-y_1}{x_2-x_1}`

Now, Let's assume that `(x_1,y_1)` is (-1,5) and `(x_2,y_2)` is (0,8).
First find the slope of line using slope formula, we get;

`m=\frac{8-5}{0-(-1)} = \frac{3}{1} = 3`

Now, plug `(x_1,y_1)` is (-1,5) and m = 3 in equation 1, we get
`(y-5)=3(x-(-1))`
or, `y-5=3(x+1)`
or, `y-5=3x+3`

Add 5 on both side, we get,
or, `y=3x+3+5`
or, `y=3x+8`

Subtract 3x on both side, we get
or, `-3x+y=8`
This is our required equation in standard form.