Question

The point slope form of the equation of the line that passes through (-4, -3) and (12, 1) is y-1=1/4(x-12) what is the standard formula equation for this line?

Answer 1

x - 4y = 8

Explanation:

The point-slope form of an equation of a line:

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

m - slope

The formula of a slope:

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

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We have the points (-4, -3) and (12, 1).

Substitute:

`m=d(1-(-3))/(12-(-4))=(4)/(16)=(1)/(4)`

Put the volume of a slope and the coordinates of the point (12, 1) to the equation of a line:

`y-1=(1)/(4)(x-12)`

The standard formula of an equation of a line:

`Ax+By=C`

Convert:

`y-1=(1)/(4)(x-12)` multiply both sides by 4

`4y-4=x-12` add 4 to both sides

`4y=x-8` subtract x from both sides

`-x+4y=-8` change the signs

`x-4y=8`