# How do you write an equation in standard form given a line that passes through (2,9) and (1,3)?

##### 1 Answer

Jun 7, 2018

#### Explanation:

#"the equation of a line in standard form is"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By=C)color(white)(2/2)|)))#

#"where A is a positive integer and B, C are integers"#

#"obtain the equation in "color(blue)"slope-intercept form"#

#•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)=(2,9)" and "(x_2,y_2)=(1,3)#

#m=(3-9)/(1-2)=(-6)/(-1)=6#

#y=6x+blarrcolor(blue)"is the partial equation"#

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

#"the partial equation"#

#"using "(1,3)" then"#

#3=6+brArrb=3-6=-3#

#y=6x-3larrcolor(red)"in slope-intercept form"#

#6x-y=3larrcolor(red)"in standard form"#