What is equation of the line in standard form that passes through (2, 7) and ( -4, 1)?

First, find the slope of the equation using

#m = (y_2 - y_1)/(x_2 - x_1)#

#m = (1-7)/(-4-2)#

#m = 1#

Second, plug in m (the slope) into the equation #y = mx +b#

So it becomes #y = 1x + b#

Plug in one of the points into the #x and y# values into the equation above and solve for #b.#

So, #(7) = 1(2) + b#

#b = 5#

Finally, plug in the #b# value into the equation to get the standard form equation.

#y = x+5" "larr# re-arrange

#x-y=-5#

#"the equation of a line in "color(blue)"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"#

#"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(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#

#"let "(x_1,y_1)=(2,7)" and "(x_2,y_2)=(-4,1)#

#rArrm=(1-7)/(-4-2)=(-6)/(-6)=1#

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

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

#"using "(2,7)" then"#

#7=2+brArrb=7-2=5#

#rArry=x+5larrcolor(red)"in slope-intercept form"#

#rArrx-y=-5larrcolor(red)"in standard form"#