Question

A line passes through the points one, four and three, -4 which is the equation of the line

Answer 1

`y = - 4x + 8`

Step-by-step explanation

The given line passes through (1,4) and (3,-4).

The slope of this line is calculated using the formula:

`m =(y_2-y_1)/(x_2-x_1)`

We substitute the points into the slope formula to get:

`m = ( - 4 - 4)/(3 - 1)`

`\implies \: m = ( - 8)/(2)`

`m = - 4`

We substitute the first point and slope into the point-slope formula

`y-y_1=m(x-x_1)`

This implies that

`y - 4 = - 4(x - 1)`

We expand to get

`y - 4 = - 4x + 4`

`y = - 4x + 2/4+ 4`

`y = - 4x + 8`