Question

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Passing through (-5,5) and the parallel to the line whose equation is y=4/5x+3/5.
--->How do I write this in point-slope form and slope-intercept form?

Answer 1

Firstly you have to find Slope without which you cannot find point-slope and slope-intercept forms as both include "Slope" in their names..

Answer 2

So, if two lines are parallel, then you must know that their slopes are equal..

Answer 3

Can you find the slope for given equation of line ie:
\[y = \frac{4}{5}x + \frac{3}{5}\]

Can you find its slope?

Answer 4

wouldn't the slope be 4/5?

Answer 5

This equation is just looking like:

\(y = mx + c\)

Yes, good the slope is \(\large \frac{4}{5}\)

Answer 6

cool so what does it have to do with the point (-5,5)?

Answer 7

Firstly we will work out for Point-slope form:

\[y - y_1 = m(x - x_1)\]

This is equation of line which passes through \((x_1, y_1)\) Point having slope \(m\)..

Answer 8

See, the point given to you is \((-5,5)\) which is nothing but \((x_1,y_1)\)

Answer 9

You know all the things now, Don't you??

Answer 10

so y+5=4/5(x+5)?

Answer 11

Check for LHS, how you got y \(\color{red}{+}\) 5 ?

Answer 12

How you got "+" in between??

Answer 13

y-5**

Answer 14

That's great..

If you write only this, then it is your "Point Slope Form"

Do you know what to do for "Slope-Intercept Form" ??

Answer 15

no because how would the point fit into y=mx+b?

Answer 16

Then how can you do it, just one step and you are there..

You got:

\[y - 5 = \frac{4}{5}(x+5)\]

How can you make it look like : \(y = ..........\) ??

Answer 17

Buddy, just add \(5\) to both the sides, and you will see, 5 will cancel out on left, and you will remain with : y = .........

Answer 18

So:

Adding \(5\), we get:

\[y = \frac{4}{5}(x+5) + 5 \implies y = \frac{4}{5}x + 4 + 5 = ??\]

Answer 19

y=4/5x+9?

Answer 20

Yep..

Answer 21

Thank you!

Answer 22

And remember, you can also solve your first equation little bit:
\[y - 5 = \frac{4}{5}(x+5) \implies \color{green}{y -5 = \frac{4}{5} + 4} \quad \quad \text{Point-Slope Form}\]

Answer 23

This will be your first equation and adding \(5\) you will get your second equation..

It is simple, so just understand the concepts and you will see you can tackle all the question similar of this kind.. :)

Welcome dear...

Answer 24

Took note of that thanks.