Respuesta :
To get the slope of this function, let's rewrite in the slope-intercept form.
The slope-intercept form have the following form:
[tex]y=mx+b_{}[/tex]where 'm' represents the slope and 'b' represents the y-intercept.
We have the following function
[tex]7x+3y=21[/tex]To rewrite in the slope-intercept form, we start with our original equation
[tex]7x+3y=21[/tex]Then, we can subtract '7x' from both sides:
[tex]\begin{gathered} 7x+3y=21 \\ 7x+3y-7x=21-7x \\ 3y=21-7x \end{gathered}[/tex]And then, finally, divide both sides by 3.
[tex]\begin{gathered} 3y=21-7x \\ \frac{3y}{3}=\frac{21-7x}{3} \\ y=\frac{21}{3}-\frac{7x}{3} \\ y=7-\frac{7x}{3} \end{gathered}[/tex]And with this, we have our final equation
[tex]y=7-\frac{7}{3}x\Leftrightarrow y=-\frac{7}{3}x+7[/tex]Done! If you compare this last equation with the general form of the line, you're going to find:
[tex]\begin{cases}m=-\frac{7}{3} \\ b=7\end{cases}[/tex]Where 'm' is the slope, and 'b' the y-intercept.
