How do you write an equation of a line given (2,0) and (4,-6)?

1 Answer
Jim G.
May 3, 2017

#y=-3x+6#

Explanation:

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

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))#

#"where m represents the slope and b, the y-intercept"#

#"to calculate the slope 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)|)))#

#"where " (x_1,y_1),(x_2,y_2)" are 2 coordinate points"#

#"the 2 points here are " (2,0)" and " (4,-6)#

#"let " (x_1,y_1)=(2,0)" and " (x_2,y_2)=(4,-6)#

#rArrm=(-6-0)/(4-2)=(-6)/2=-3#

#rArry=-3x+b#

#"to find b, use either of the 2 given points"#

#"using " (2,0)" substitute into equation to find b"#

#rArr0=(-3xx2)+brArrb=6#

#rArry=-3x+6larrcolor(red)" is equation of line"#

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