How do you find the slope and intercept of #5 - 1/3y = 2x#?

1 Answer
Aug 28, 2016

Answer:

slope = - 6 , y-intercept = +15

Explanation:

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

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

The advantage to having the equation in this form is that m and b , may be extracted 'easily'.

Rearrange #5-1/3y=2x" in this form"#

subtract 5 from both sides.

#rArrcancel(5)-cancel(5)-1/3y=2x-5rArr-1/3y=2x-5#

multiply through by - 1 : #1/3y=-2x+5#

now multiply both sides by 3.

#rArrcancel(3)^1xx1/cancel(3)^1 y=-6x+15rArry=-6x+15#

The equation is now in the form #color(blue)(y=mx+b)#

#rArr"slope" =-6" and y-intercept" =+15#
graph{-6x+15 [-45.63, 45.6, -22.74, 22.9]}