Question

How do you find a standard form equation for the line with (-6, 0) and (2, -9)?

Answer 1

`y=-9/8x-27/4`

Explanation:

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

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))`
where m represents the slope and b, the y-intercept.

We have to find the values of m and b.

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

`color(red)(|bar(ul(color(white)(a/a)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(a/a)|)))`
where `(x_1,y_1)" are 2 coordinate points"`

here the 2 points are (-6 ,0) and (2 ,-9)

let `(x_1,y_1)=(-6,0)" and " (x_2,y_2)=(2,-9)`

`rArrm=(-9-0)/(2+6)=(-9)/8=-9/8`

We can now write a partial equation as `y=-9/8x+b`

To calculate b, use either of the 2 given points that lie on the line.

Using (2 ,-9)That is x= 2 and y = -9 , substitute in partial equation

`rArr(-9/8xx2)+b=-9rArr-9/4+b=-9rArrb=-27/4`

`rArry=-9/8x-27/4" is the equation of the line"`