Respuesta :
Answer:
[tex]-\dfrac32[/tex]
Step-by-step explanation:
To get the slope-intercept form with the gradient [tex]m[/tex], we have to rearrange [tex]3x+2y=7[/tex] into an equation that looks like this: [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.
[tex]3x+2y=7\implies 2y=7-3x\implies \boxed{y=-\dfrac32x+\dfrac72}[/tex]
Therefore the gradient is [tex]-\dfrac32[/tex].
Fun fact:
If you want to go from standard form (Ax+By=C) to slope-intercept form (y=mx+b), all you have to do is write m and b in terms of A, B and C. This is my working out on how to do that.
(basically just rearrange Ax+By=C so that it looks like y=mx+b)
[tex]Ax+By=C\implies By=C-Ax\implies \boxed{y=\dfrac CB-\dfrac ABx}[/tex]
You don't have to remember this, it's just a fun fact :)
