How do you write an equation of a line that has the same slope as the line #3x-5y=7# and the same #y#-intercept as the line #2y-9x=8#?

1 Answer
Jim G.
May 10, 2018

#3x-5y=-20#

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"#

#"rearrange both given equations into this form and extract"#
#"m and b from them"#

#3x-5y=7#

#rArr-5y=-3x+7#

#rArry=3/5x+7/5larrcolor(blue)"in slope-intercept form"#

#"with "m=3/5larrcolor(red)"the required slope"#

#2y-9x=8rArr2y=9x+8#

#rArry=9/2x+4larrcolor(blue)"in slope-intercept form"#

#"with "b=4larrcolor(red)"the required y-intercept"#

#rArry=3/5x+4larrcolor(magenta)"in slope-intercept form"#

#"multiply all terms by 5 and rearrange"#

#rArr5y=3x+20#

#rArr3x-5y=-20larrcolor(magenta)"in standard form"#

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