What is the slope and the #y#-intercept of #2x+3y=12#?

Answer 1

The slope is #color(red)(m = -2/3#

The y-intercept is #color(blue)(b = 4)#

To find the slope and y-intercept we need to put this equation into slope-intercept form. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

Solving for #y# gives:

#-color(red)(2x) + 2x + 3y = -color(red)(2x) + 12#

#0 + 3y = -color(red)(2x) + 12#

#3y = -2x + 12#

#(3y)/color(red)(3) = (-2x + 12)/color(red)(3)#

#(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = (-2x)/color(red)(3) + 12/color(red)(3)#

#y = color(red)(-2/3)x + color(blue)(4)#

Therefore:

The slope is #color(red)(m = -2/3#

The y-intercept is #color(blue)(b = 4)#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.