How do you write an equation in point slope and slope intercept form given (1, 2) and (2, 5)?

1 Answer
Jim G.
May 23, 2018

#y-2=3(x-1)" and "y=3x-1#

Explanation:

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

#•color(white)(x)y-y_1=m(x-x_1)#

#"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(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#"let "(x_1,y_1)=(1.2)" and "(x_2,y_2)=(2,5)#

#m=(5-2)/(2-1)=3#

#"using "m=3" and "(x_1,y_1)=(1,2)" then"#

#y-2=3(x-1)larrcolor(red)"in point-slope form"#

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

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

#"distributing and rearranging gives"#

#y-2=3x-3#

#y=3x-1larrcolor(red)"in slope-intercept form"#

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