Question

Consider the line with `x`-intercept of 2 and `y`-intercept of -2. What is the equation of this line in standard form?

Answer 1

`y=x-2`

Explanation:

An x-intercept of two means we have the point

`(2,0)`

A y-intercept of negative two means we have the point

`(0,-2)`

Recall the formula of the slope of a line:

`m=(y_2-y_1)/(x_2-x_1)`

Since we have two points, we can calculate the slope using ( `(x_1,y_1)=(2,0), (x_2,y_2)=(0,-2)`

`m=(-2-0)/(0-2)`

`m=1`

The point-slope form of a line is:

`y-y_1=m(x-x_1)`

Where `(x_1,y_1)` is a point through which the line passes and `m` is the slope.

We already have m; we can use either of our points for `(x_1,y_1)`, let's use `(2,0)`.

`y-0=1(x-2)`
`y=x-2`

Answer 2

`x-y=2`

Explanation:

`"the equation of a line in "color(blue)"standard form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By=C)color(white)(2/2)|)))`

`"where A is a positive integer and B, C are integers"`

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"to calculate m use the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(2,0)" and "(x_2,y_2)=(0,-2)`

`rArrm=(-2-0)/(0-2)=1`

`rArry=x+blarrcolor(blue)"is the partial equation"`

`"y-intercept "=(0,-2)rArrb=-2`

`rArry=x-2larrcolor(red)"in slope-intercept form"`

`rArrx-y=2larrcolor(red)"in standard form"`