How do you graph the function #y=-2/3x+4#?

1 Answer
Jan 23, 2017

There are several strategies you can use to approach this, but since the given equation is in slope-intercept form, let's take advantage of that.

When the equation of a line is given in the form of
#y = color(purple)(m)x + color(blue)(b)#, then

#color(purple)(m) =# the slope of the line #(color(purple)(m)=(Delta y)/(Delta x))# and
#color(blue)(b) =# the y-intercept or where the line crosses the #y#-axis

Since we know that #color(blue)(b) = 4#, we know the line crosses the #y#-axis at #y=4#. In other words, the line passes through the point #(0,4)#.

Then, applying the slope to that point, we can find a second point on the line.

#color(purple)(m) = (Delta y)/(Delta x) = -2/3 = (-2)/3 = 2/-3#

This tells us that when #x# changes by #3# units (#Delta x#), #y# changes by #-2# units (#Delta y#)

Starting at #(0,4)#, we can apply the slope:

#Delta x = 3 = x_2 - 0 => x_2 = 3#
#Delta y = -2 = y_2 - 4 => y_2 = 2#

The point #(3,2)# will be on the line. Plotting these two points #(0,4)# and #(3,2)# and drawing a straight line through these points will give you the graph of the function #y=-2/3+4#