How do you write an equation in standard form for a line that goes through (5, –2) and (–5, 4)?

1 Answer
Aug 6, 2018

3x+5y=53x+5y=5

Explanation:

"the equation of a line in "color(blue)"standard form"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"

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

•color(white)(x)y=mx+c

"where m is the slope and c 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)=(-5,4)

m=(4-(-2))/(-5-5)=6/(-10)=-3/5

y=-3/5x+clarrcolor(blue)"is the partial equation"

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

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

-2=-3+crArrc=-2+3=1

y=-3/5x+1larrcolor(red)"in slope-intercept form"

"multiply all terms by 5"

5y=-3x+5

"add "3x" to both sides"

3x+5y=5larrcolor(red)"in standard form"