Additional intercept form problems.

[jamescv31]

Hello, I'm here for another related intercept form problem of the formula: \(\displaystyle \displaystyle \frac{x}{a} + \frac{y}{b} \:=\:1\)

a) Find the equation of the line passing through (-5,-7) AND with y-intercept 3.

b) Find the equation of the line passing with x-intercept 1/3 and y-intercept 2/5.

I'm not sure how this solution will be, I need this as my reference pattern.

Thank you.

Note: In letter B I couldn't figured since its a fraction and the way of having an LCD might be unsure of the correct equation so really need an informative information.

Also in Letter A, we don't have an example related for that.

 

[MarkFL]

For part a) I would begin with the slope-intercept form, using the given intercept of 3:

\(\displaystyle y=mx+3\)

Now, use the given point $(x,y)=(-5,-7)$ and you will then be able to solve for $m$:

\(\displaystyle -7=m(-5)+3\)

For part b) I would use the two-intercept form you cited, and recall the "invert and multiply" rule for division by fractions:

\(\displaystyle \frac{c}{d/e}=c\cdot\frac{e}{d}=\frac{ce}{d}\)

Can you proceed with a) and b) now? Please feel free to post your progress. :D

 

[jamescv31]

Here's my progress, in letter a)

is it an M as slope only? not the whole equation? because the answer of my M is 2.

Then on letter B my equation answers as \(\displaystyle 6x+5y-30=0\)?

 

[MarkFL]

Here's my progress, in letter a)

is it an M as slope only? not the whole equation? because the answer of my M is 2.

Then on letter B my equation answers as \(\displaystyle 6x+5y-30=0\)?

Yes, $m=2$, and so your line is:

\(\displaystyle y=2x+3\)

For part b) that isn't quite correct. Can you show your work so we can see where you went wrong?

 

[jamescv31]

I'm not sure on how the "invert and multiply" works.

\(\displaystyle x/1/3 + y/2/5 = 1

x/5 + y/6 =1 \) I made like a cross multiplication it becomes

\(\displaystyle 6x + 5y = 30\) then made an LCD to obtain the

 

[MarkFL]

You use cross multiplication when you have two fractions that are equal to one another. What you want to do here is:

\(\displaystyle \frac{x}{1/3}+\frac{y}{2/5}=1\)

Invert and mutliply:

\(\displaystyle x\frac{3}{1}+y\frac{5}{2}=1\)

Multiply through by 2:

\(\displaystyle 6x+5y=2\)