How do you write the equation of a line in point slope form and slope intercept form given points (-1, -5) (-7, -6)?

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Answer 1 · 2018-03-20T11:35:56

The equation of the line in slope intercept form is $y= 1/6x-29/6.$
The equation of line in point slope form is $y+5=1/6(x+1)$

The slope of the line passing through

$(-1,-5) and (-7,-6)$ is

$m= (y_2-y_1)/(x_2-x_1)= (-6+5)/(-7+1)= (-1)/-6=1/6$

Let the equation of the line in slope intercept form be

$y=mx+c or y=1/6*x+c$ . The point $(-1,-5)$ will satisfy

the equation .So, $-5= 1/6*(-1)+c$ or

$c= -5+1/6=(-29)/6$ . Hence the equation of the line in

slope intercept form is $y= 1/6x-29/6.$

The equation of line in point slope form passing through

$(x_1,y_1)$ having slope of $m$ is $y-y_1=m(x-x_1)$ .

The equation of line passing through $(-1,-5)$ having slope of

$1/6$ is $y+5=1/6(x+1)$ [Ans]