Answer :
Answer:
Explanation:
The standard form of a linear equation is
[tex]Ax+By=C[/tex]However, it is a lot easier if we find the equation in slope-intercept form
[tex]y=mx+b[/tex]and then rearrange the above equation to write it in standard form.
We are told that the slope of the line is 2/3 which means m = 2/3; therefore, the above equation becomes
[tex]y=\frac{2}{3}x+b[/tex]Moreover, fro the point (-5, 1) we know that when x = -5, then y = 1; therefore, the above equation gives
[tex]1=\frac{2}{3}(-5)+b[/tex]Simplifying the above gives
[tex]1=-\frac{10}{3}+b[/tex]adding 10/3 to both sides gives
[tex]1+\frac{10}{3}=-\frac{10}{3}+b+\frac{10}{3}[/tex][tex]\begin{gathered} \frac{3}{3}+\frac{10}{3}=b \\ \\ \end{gathered}[/tex][tex]\therefore b=\frac{13}{3}[/tex]With the value of b in hand, we write the slope-intercept of the equation:
[tex]y=\frac{2}{3}x+\frac{13}{3}[/tex]Now, to write the above in standard form, we multiply both sides by 3. This cancels out 3 in the denominator on the right-hand side and gives
[tex]3y=2x+13[/tex]Finally, subtracting 2x from both sides gives
[tex]3y-2x=13[/tex]Just shift the position of the terms on the left-hand the side and we get
[tex]\boxed{-2x+3y=13.}[/tex]which is the standard form of our equation!