Question

Find the equation of the line
passing through the points (3,1) and (7,-7)

Answer 1

y = -2x+7

Explanation:

equation of line formula:

`y = mx + c`

m = slope, c = y-intercept

1) find the slope using the given coordinates

slope formula:

`(y2 - y1)/(x2 - x1)`

i) (3,1)

x1=3

y1=1

ii) (7,-7)

x2=7

y2=-7

substitute the values into the formula

`m = ( - 7 - 1)/(7 - 3)`

`m = ( - 8)/(4)`

`m = - 2`

so now half of the equation is complete as we have the the value of m. substitute the value of m into the slope formula.

`y = - 2x + c`

2) find the value of c

to find the value of c, we must substitute either coordinate into the half equation. so, i choose the coordinate (3,1). if you substitute the coordinate (7,-7) , you will get the same value of c.

(3,1)

x = 3

y = 1

`y = - 2x + c`

`1 = - 2(3) + c`

`1 = - 6 + c`

`1 + 6 = c`

`c = 7`

substitute the value of c into the half equation and that is your straight line equation

`y = - 2x + 7`