How do you write #2x-3y= 15# in slope-intercept form and graph it?

1 Answer
Mar 24, 2017

Answer:

#y=2/3x-5#

Explanation:

The equation of a line in #color(blue)"slope-intercept form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))#
where m represents the slope and b, the y-intercept.

#"Rearrange " 2x-3y=15" into this form"#

subtract 2x from both sides.

#cancel(2x)cancel(-2x)-3y=-2x+15#

#rArr-3y=-2x+15#

divide ALL terms on both sides by - 3

#(cancel(-3) y)/cancel(-3)=(-2)/(-3)x+15/(-3)#

#rArry=2/3x-5larrcolor(red)" in slope-intercept form"#

The y-intercept is - 5# larrcolor(red)" 1 point on the graph"#

#"choose " x=3" and find y"#

#x=3toy=(2/3xx3)-5=2-5=-3#

#rArr(3,-3)larrcolor(red)" is a point on the graph"#

Plot the 2 points and draw a straight line through them and you have the graph.
graph{2/3x-5 [-10, 10, -5, 5]}