Can someone check my answers please? I'm really struggling with this.
Write an equation in point-slope form for the line through the given point with the given slope.

- anonymous

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- anonymous

(8,3); m=6 (1 point)
y+3=6(x-8)
y-3=6(x-8)
y-3=6(x+8) <-- My answer.
y+3=6x+8

- SolomonZelman

\(\LARGE y-\color{green}{y_1}=\color{blue}{\rm m}(x-\color{red}{x_1})\)
where your point is
\(\LARGE \left(\color{red}{x_1},\color{green}{y_1}\right)\)
and your slope is
\(\LARGE \rm \color{blue}{m}\)

- SolomonZelman

in this case: \(x_1=8\) and \(y_2=3\)
The slope is \(\rm m\)

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## More answers

- SolomonZelman

and in this case, the slope is 6 (i.e. m=6)

- anonymous

So, if I understand what you're saying, the answer should be B instead of C?

- anonymous

if a line has a slope \(m\) and passes through a point \(x_0,y_0\) then the slope between any other point on the line \((x,y)\) and the given point \((x_0,y_0)\) must be \(m\), i.e. $$\text{slope between }(x,y)\text{ and }(x_0,y_0)=m\\\frac{y-y_0}{x-x_0}=m\\y-y_0=m(x-x_0)$$

- SolomonZelman

Yes B is correct! VEry good!

- anonymous

so in this case our given point is \((8,3)\) and our slope is \(6\). for any other point \((x,y)\) on our line we require that the slope between \((x,y)\) and \((8,3)\) is \(6\), so:$$\frac{y-3}{x-8}=6\\\text{so multiplying both sides by }x-8\text{ gives us: }y-3=6(x-8)$$... and this is the point-slope form

- anonymous

Thank you, would you mind checking a few more? I have two days to finish and I'm terrified of getting a bad grade.

- SolomonZelman

Yes, I think I can check more problems...
and of course, N☼ PR☼BLEM

- anonymous

now this is an unrelated, tangential note to help connect this with slope-intercept form: suppose the given point is a \(y\)-intercept, i.e. a point whose \(x\)-coordinate is zero; we can write this \((0,b)\). if we're given this \(y\)-interept and a slope \(m\), we'll find the following equation by point-slope form:$$y-b=m(x-0)$$simplifying since \(x-0=x\) we have:$$y-b=mx\\y=mx+b$$which is the normal slope-intercept form that you're familiar with

- anonymous

2. Graph the equation.
y+5=-2(x-4)

- anonymous

I'll attach the graphs.

- anonymous

unrelated note continued: in fact, given a point-slope form equation \(y-y_0=m(x-x_0)\) there is a natural way to rewrite in slope-intercept form -- simply distribute everything out and get \(y\) alone on one side: $$y-y_0=m(x-x_0)\\y-y_0=mx-mx_0\\y=\color{blue}mx+\underbrace{\color{red}{y_0-mx_0}}_{b}\\y=mx+b$$

- SolomonZelman

if you got the graph why are you asked to graph it? :O

- SolomonZelman

It will be easier if we go ahead and simplify this equation written in a point slope form, INTO, a y-intercept form (i.e. y=mx+b).

- SolomonZelman

y+5=2(x-4)
1. expand the left side)
2. subtract 5 from both sides

- SolomonZelman

oh, -2.... I missed that. apologize.

- SolomonZelman

ok, you can exclude option c, because it is going up and the line with a negative slope is always going down.

- SolomonZelman

y+5=-2(x-4)
you can re-write it into a s y-intercept form, but you don't really have to.
you know the line should go down by 2 units every time it goes 1 unit to the right (that is what a slope of -2 means). What you don't know is where do you start.... plug in x=0, to find the y-interecept.

- SolomonZelman

(I mean I can tell a negative slope that is -2, and a negative slope that is not as steep as -2 right away, tho' so you can just look at the graph to see the option (the only one option) that goes 2 units down every time it goes 1 unit to the right.)

- anonymous

Possibly B?

- SolomonZelman

B is more like going 2 units to the right as it goes 1 down,
but a slope of -2 means that we go down by 2 each time we go 1 to the right

- anonymous

Then it has to be A, because I don't think D is anywhere near what we're looking at.

- SolomonZelman

yes

- SolomonZelman

A is Correct

- anonymous

Do you have time to help with a few more?

- SolomonZelman

(I am just showing an SAT kind of a technique where you can quickly identify the answer and exclude other options just using a quick look/analysis)

- SolomonZelman

yes, I think so...

- anonymous

Which point is located on the line represented by the equation y+4=-5(x-3)?
(-4,-5)
(-5,-4)
(3,-4) <-- My answer.
(-3,4)

- SolomonZelman

Recall the point slope formula rule.
I will rewrite your equation for you real quick.
y-(-4)=-5(x-3)
now compare that to
y-y1=m(x-x1)

- SolomonZelman

Yes, your answer is right

- anonymous

##### 1 Attachment

- anonymous

I think D would be the correct answer for that one.

- SolomonZelman

Are you sure?
I am asking that because the line is not going down, it si going up....

- SolomonZelman

It does go by 2 units vertically, as it goes 1 unit to the right.
BUT it goes 2 units (vertically) up, not (vertically) down....

- anonymous

OH! Okay! So A would be correct.

- SolomonZelman

Yup

- anonymous

I'm really hoping that I'm right about this one, but I think it's A.

##### 1 Attachment

- SolomonZelman

you got "fooled" (excuse me) by the look of it.

- SolomonZelman

|dw:1436469019837:dw|

- anonymous

Possibly D?

- SolomonZelman

see it perfectly goes 3 units down, as it goes 8 units to the right
(and although it is close to the slope of 1/2)

- SolomonZelman

-8/3 slope, means:
Your graph goes 8 units down as it goes 3 units to the right
-3/8 slope, means:
Your graph goes 3 units down as it goes 8 units to the right
which one is correct if you look on our graph?

- anonymous

C, I believe.

- SolomonZelman

it wuld be C if it was going UP by 3 while going 8 to the right.
But it goes DOWN by 3 while it goes 8 to the right.
So m=-3/8

- anonymous

Then it must be D.

- SolomonZelman

it is B

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