Question

How do you write the standard form of a line given (3,-2) and (7,6)?

Answer 1

y = 2x - 8

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 require to find m and b to obtain the equation.

To find 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)" and " (x_2,y_2)" are 2 points".`

The 2 coordinate points here are (3 ,-2) and (7 ,6)

let `(x_1,y_1)=(3,-2)" and " (x_2,y_2)=(7,6)`

`rArrm=(6-(-2))/(7-3)=8/4=2`

We now have a partial equation: y= 2x + b and to find b use either of the 2 given coordinate points.

Using (7 ,6) and substituting x = 7 , y = 6 into the partial equation.

`: 6 =(2xx7)+brArr14+b=6rArrb=6-14=-8`

`rArry=2x-8" is the equation"`