How do you write an equation in standard form for a line which passes through points (-1,-1) and (1,3)?

1 Answer
Jul 2, 2018

2x-y=-1

Explanation:

"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"

"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)=(-1,-1)" and "(x_2,y_2)=(1,3)

m=(3-(-1))/(1-(-1))=4/2=2

y=2x+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=2+brArrb=3-2=1

y=2x+1larrcolor(red)"in slope-intercept form"

"rearranging gives"

2x-y=-1larrcolor(red)"in standard form"