How do you find the slope and intercept of #3x-2y=9#?

Question

Genesis Allen · Accepted Answer

See a solution process below:

This equation is in Standard Linear Form. The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)# Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1 #color(red)(3)x + (color(blue)(-2))y = color(green)(9)# The slope of an equation in standard form is: #m = -color(red)(A)/color(blue)(B)# Substituting gives: #m = -color(red)(3)/color(blue)(-2) = 3/2# The #y#-intercept of an equation in standard form is: #color(green)(C)/color(blue)(B)# Substituting gives: #color(green)(9)/color(blue)(-2) = -9/2# or #(0, -9/2)#

Ethan Adkins · Answer

undefined To find the slope and y-intercept of the equation $3x - 2y = 9$, rearrange it into slope-intercept form $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. First, solve for $y$: $2y = 3x - 9$. Then divide by 2: $y = \frac{3}{2}x - \frac{9}{2}$. Comparing with $y = mx + b$, the slope $m$ is $ \frac{3}{2} $ and the y-intercept $b$ is $ -\frac{9}{2} $. So, the slope is $ \frac{3}{2} $ and the y-intercept is $ -\frac{9}{2} $.