MHB Help converting two standard form equations to slope intercept form?

[matheus]

Hi guys,

I have a few tries at this but I keep coming up wrong, so can anyone show me how to convert these two standard form equations into slope intercept form?

2x - 11y = 2,
-6x + 3y = 9.

Greatly appreciate any help offered :)

Thank you!

 

[MarkFL]

Hello matheus! :D

I have moved your thread as this is a topic for elementary algebra. ;)

Now, if we are given a linear equation in standard form:

$$Ax+By=C$$

And we wish to write this in slope-intercept form $y=mx+b$, we need to solve for $y$. So, we first subtract $Ax$ from both sides to get:

$$By=-Ax+C$$

And now we need to divide through by $B$ and we have:

$$y=-\frac{A}{B}x+\frac{C}{B}$$

Now we have a formula we can use. For example, if we are given:

$$2x+3y=5$$

We identify:

$$A=2,\,B=3,\,C=5$$

And, using our formula, we may state this equation in slope-intercept form as:

$$y=-\frac{2}{3}x+\frac{5}{3}$$

Can you apply the formula to your two problems?

 

[matheus]

Hi MarkFL :D

Wow thank you so much for your very helpful reply!

I have given it a go to try and apply that method to my two equations, can you have a look and tell me how I did?

I am new to studying algebra so these basic lessons are helping me so much :D

 

[MarkFL]

It looks like you did well! (Yes)

 

[matheus]

Awesome! Thank you MarkFL :D

Just out of interest, would you have done it the same way as I did?

 

[MarkFL]

Awesome! Thank you MarkFL :D

Just out of interest, would you have done it the same way as I did?

Yes...but once I had a few semesters of math under my belt, I began to recognize that the assigned problems in a homework set were all similar, and so I would develop a general formula as I did in my first post, and then I would simply plug in the data for each problem. Solve once, then plug and play. :D

 

[matheus]

That's so smart! :-D

Just one more thing, do you happen to know of any online calculator that converts equations into slope form?

Not to cheat of course, that won't help me at all, just to check answers really :-)

 

[MarkFL]

That's so smart! :-D

Just one more thing, do you happen to know of any online calculator that converts equations into slope form?

Not to cheat of course, that won't help me at all, just to check answers really :-)

Yes, try this site:

2x-11y'='2 in slope-intercept form - Wolfram|Alpha

 

[matheus]

Excellent! :D Thanks again for all your help, I am very grateful of helpful people like you sir. Keep up the good work!