How do you write the point slope form of the equation given (-5,-1) and (4,-7)?

1 Answer
Jim G.
Nov 1, 2017

#y+7=-2/3(x-4)#

Explanation:

#"the equation of a line in "color(blue)"point-slope form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))#

#"where m is the slope and "(x_1,y_1)" a point on the line"#

#"to calculate m use the "color(blue)"gradient formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#

#"let "(x_1,y_1)=(-5,-1)" and "(x_2,y_2)=(4,-7)#

#rArrm=(-7-(-1))/(4-(-5))=(-6)/9=-2/3#

#"use either of the 2 points for "(x_1,y_1)#

#"using "(x_1,y_1)=(4,-7)#

#y-(-7)=-2/3(x-4)#

#rArry+7=-2/3(x-4)larrcolor(red)" in point-s;ope form"#

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