# What is the equation of the line between #(5,2)# and #(-1,3)#?

##### 1 Answer

Apr 15, 2018

#### Explanation:

#"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"#

#"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)=(5,2)" and "(x_2,y_2)=(-1,3)#

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

#rArry=-1/6x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute either of the 2 given points into"#

#"the partial equation"#

#"using "(5,2)" then"#

#2=-5/6+brArrb=12/6+5/6=17/6#

#rArry=-1/6x+17/6larrcolor(red)"in slope-intercept form"#