Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
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!
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
