Question

How do you write the equation in slope intercept form given (5, 1), (0, -6)?

Answer 1

`y=7/5x-6`

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.

To obtain the equation, we require to find 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)" and " (x_2,y_2)" are 2 points"`

The 2 points here are (5 ,1) and (0 ,-6)

let `(x_1,y_1)=(5,1)" and " (x_2,y_2)=(0 ,-6)`

`rArrm=(-6-1)/(0-5)=(-7)/(-5)=7/5`

We are given the point (0 ,-6) which is the point where the line crosses the y-axis, hence the y-intercept b = -6

`rArry=7/5x-6" is the equation in slope-intercept form."`