How do you write an equation in point slope and slope intercept form given (2,3) with x-intercept 4?

1 Answer
Apr 19, 2018

#y-3=-3/2(x-2)" and "y=-3/2x+6#

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)=(2,3)" and "(x_2,y_2)=(4,0)#

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

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

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

#"distribute and rearrange"#

#y-3=-3/2x+3#

#rArry=-3/2x+6larrcolor(red)"in slope-intercept form"#