Question

How do you write an equation in slope intercept form of a line containing the coordinates (7,4) and (14,8)?

Answer 1

`y=4/7x`

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 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 (7 ,4) and (14 ,8)

let `(x_1,y_1)=(7,4)" and " (x_2,y_2)=(14,8)`

`rArrm=(8-4)/(14-7)=4/7`

The equation can be partially written as `y=4/7x+b`

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

Using (7 ,4). That is x = 7 and y = 4

`rArr4=(4/7xx7)+brArr4=4+brArrb=0`

`rArry=4/7x" is the equation in slope-intercept form"`