How do you graph #5/6x - 6y = 8# by plotting points?

Question

Eva Adamson · Accepted Answer

Pick values for #x# and solve for #y#

Only 2 points are needed to graph a line, but additional points can be used to check your answer.

To eliminate the need to deal with fractions, we can multiply all terms of the equation by 6: #color(red)((6))5/6x-color(red)((6))6y=color(red)((6))8# #5x-36y=48# Re-write the equation so that it is in the form #y=...# #5x-36y=48# #5x-36ycolor(red)(+36y)color(blue)(-48)=48color(blue)(-48)color(red)(+36y)# #5x-48=36y# #(5x-48)/color(red)(36)=(36y)/color(red)(36)# #y=(5x-48)/36# Pick values for #x# and calculate the corresponding value for #y# Let #x=-5# #y=(5(color(red)(-5))-48)/36 => y=-2.084# Let #x=0# #y=(5(color(red)(0))-48)/36 => y=-1.333# Let #x=5# #y=(5(color(red)(5))-48)/36 => y=-0.639# Plot these points and connect with a straight line graph{5/6x-6y=8 [-10, 10, -5, 5]}

Isaiah Anthony · Answer

undefined To graph the equation 5/6x - 6y = 8 by plotting points:

1. Choose values for x and solve for y to find corresponding points.
2. Plot these points on a coordinate plane.
3. Draw a straight line through the plotted points.

Alternatively, you can rearrange the equation into slope-intercept form (y = mx + b) to find the y-intercept and slope, and then use this information to plot the line.