How do you find the slope and y-intercept for the graph of the equation: 9x - 3y = 81?

Question

Ethan Adkins · Accepted Answer

graph{y = 3x - 27 [-5, 10, -30, 5]}

The slope is #color(red)(3)# and the y-intercept is #color(blue)(-27)# or (#color(blue)(0, -27)#)

To find the slope and y-intercept of this equation we must transform it into the 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. We can solve this equation for #y# to transform the equation we have been given in this problem into this form: #9x - 3y = 81# #9x - color(red)(9x) - 3y = color(red)(-9x) + 81# #0 - 3y = color(red)(-9x) + 81# #-3y = - color(red)(-9x) + 81# #(-3y)/color(green)(-3) = (color(red)(-9x) + 81)/color(green)(-3)# #(color(green)(cancel(color(black)(-3)))y)/cancel(color(green)(-3)) = (color(red)(-9x) + 81)/color(green)(-3)# #y = (color(red)(-9x) + 81)/color(green)(-3)# #y = color(red)(-9x)/color(green)(-3) + 81/color(green)(-3)# #y = 3x - 27# Therefore the slope is #color(red)(3)# and the y-intercept is #color(blue)(-27)# or (#color(blue)(0, -27)#)

Eli Assouline · Answer

undefined To find the slope and y-intercept for the graph of the equation 9x - 3y = 81, first, solve the equation for y to put it in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.

Starting with 9x - 3y = 81:
1. Subtract 9x from both sides: -3y = -9x + 81.
2. Divide both sides by -3 to isolate y: y = 3x - 27.

Now, the equation is in slope-intercept form, where the slope (m) is 3, and the y-intercept (b) is -27.