What is the equation of the line that passes through $(-3,4)$ and $(-1, -2)$ ?

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Answer 1 · 2018-03-03T13:31:15

$y + 3x + 5 = 0$

$color(red)(x_1->-3)$
$color(red)(x_2->-1)$
$color(red)(y_1->4)$
$color(red)(y_2->-2)$

The equation of a line is equal to:-

$color(green)[y-y_1=(y_1 - y_2)/(x_1-x_2) xx (x-x_1)]$

Put the above values in this equation.

You get

$color(brown)[y-4 = (4-(-2))/(-3-(-1)) xx [x-(-3)]]$

$color(brown)[=> y-4 = (4+2)/(-3+1) xx (x+3)]$

$color(purple)[=> y-4 = 6/-2 xx (x+3)]$

$color(purple)[=> y-4 = -3 xx (x+3)]$

$color(blue)[=> y-4 = -3x -9]$

$color(blue)[=> y + 3x -4 + 9 = 0]$

$color(orange)[=> y + 3x + 5 = 0]$

What is the equation of the line that passes through (-3,4)(-3,4) and (-1, -2)(-1, -2)?