# What is the equation of the line passing through #(1,4)# and #(-8,2)#?

##### 1 Answer

Apr 17, 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)=(1,4)" and "(x_2,y_2)=(-8,2)#

#rArrm=(2-4)/(-8-1)=(-2)/(-9)=2/9#

#rArry=2/9x+blarrcolor(blue)"is the partial equation"#

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

#"the partial equation"#

#"using "(1,4)" then"#

#4=2/9+brArrb=36/9-2/9=34/9#

#rArry=2/9x+34/9larrcolor(red)"is the equation of the line"#