Question

Write the standard form equation of the line through the given points. through (0.-4) and (-3,-2)

Answer 1

The standard form of equation of the line through the given points. through (0.-4) and (-3,-2) is
`(2)/(3)x+y=-4`

Explanation:

The standard form of equation is
`Ax+By=C`

Finding slope

Using the given points (0,-4) and (-3,-2) we can find slope using formula:
`Slope=(y_2-y_1)/(x_2-x_1)`

`Slope=(-2-(-4))/(-3-(0))\\Slope=(-2+4)/(-3) \\Slope=-(2)/(3)`

Finding y-intercept

Using point (0,4) and Slope=-2/3 we can find y-intercept

`y=mx+b\\-4=-(2)/(3)(0)+b\\-4=0+b\\b=-4`

The slope intercept form of the line through the given points. through (0.-4) and (-3,-2) having slope =-2/3 and b=-4 will be:

`y=mx+b\\y=-(2)/(3)x-4`

Now, standard form of equation will be:
`(2)/(3)x+y=-4`

So, The standard form of equation of the line through the given points. through (0.-4) and (-3,-2) is
`(2)/(3)x+y=-4`