How do you find the slope and intercept of #y=2/3(2x-4)#?

Question

Hazel Anglin · Accepted Answer

Expand the bracket and then compare to the general equation for a straight line, #y=mx+c#.

The given equation represents a straight line. We can express any straight line as follows in an equation: #y=mx + c# What does this mean? The variables are denoted by the letters #y# and #x# as usual. The slope of the line, or its steepness, is indicated by the letter #m#. A positive slope indicates that the line slopes upward; a negative slope indicates that it slopes downward. Lastly, the letter #c# indicates the point at which the line crosses the #y#-axis, also known as the #y#-intercept. Let's examine the given equation in more detail. #y=2/3(2x-4)# The two terms in this bracket, #2x# and #-4#, are all multiplied by #2/3#. This is not the desired #mx+c# form, so let's expand the bracket to see what we get: #y=(4x)/3-8/3# #y=2/3*2x-2/3*4# The term without #x# in it is our #y#-intercept, #c#. Now compare this to the general equation for a straight line, #y=mx+c#. You can see that #m=4/3# since that's what the #x# is being multiplied by. #c=-8/3# and #m=4/3# We determine that this line crosses the #y#-axis at a height of #-8/3#, or #-2.6# recurring, and has a slope of #4# in #3#.

Jace Anderson · Answer

undefined To find the slope-intercept form of the equation $ y = \frac{2}{3}(2x - 4) $, we first need to distribute the $\frac{2}{3}$ into the parentheses:

$ y = \frac{4}{3}x - \frac{8}{3} $

Now, the equation is in the form $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept.

So, the slope is $ \frac{4}{3} $, and the y-intercept is $ -\frac{8}{3} $.