Respuesta :
We are asked to find the equation of the line that has the same slope as the equation below
[tex]6x+3y=12[/tex]And it passes through the point (2, 1)
Let us first re-write the given equation into the slope-intercept form.
To do that, simply separate out the y variable.
[tex]\begin{gathered} 6x+3y=12 \\ 3y=-6x+12 \\ y=-\frac{6x}{3}+\frac{12}{3} \\ y=-2x+4 \end{gathered}[/tex]The standard slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Comparing the standard form with the above equation we see that
Slope = m = -2
So, the equation of the line that we want to find out becomes
[tex]y=-2x+b[/tex]Now we need to find out the value of y-intercept (b)
Since it is given that the line passes through the point (2, 1) so we can substitute it into the above equation and solve for b.
[tex]\begin{gathered} y=-2x+b \\ 1=-2(2)+b \\ 1=-4+b \\ 1+4=b \\ 5=b \end{gathered}[/tex]So, the value of the y-intercept is 5
Therefore, the equation of the line is
[tex]y=-2x+5[/tex]