Question

How do you write an equation in slope intercept form of a line containing the points (3,7) , (6,8)?

Answer 1

`y=1/3x+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.

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 coordinate points"`

The 2 points here are (3 ,7) and (6 ,8)

let `(x_1,y_1)=(3,7)" and " (x_2,y_2)=(6,8)`

`rArrm=(8-7)/(6-3)=1/3`

We can write the partial equation as `y=1/3x+b`

To find b, substitute the coordinates of either of the 2 points into the partial equation and solve for b.

Using the point (3 ,7) that is x = 3 and y = 7

`rArr(1/3xx3)+b=7rArr1+b=7rArrb=6`

Thus `y=1/3x+6" is equation in slope-intercept form"`