Question

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.

Answer 1

(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

Answer 2

\(\LARGE y-\color{green}{y_1}=\color{blue}{\rm m}(x-\color{red}{x_1})\)


where your point is
\(\LARGE \left(\color{red}{x_1},\color{green}{y_1}\right)\)

and your slope is
\(\LARGE \rm \color{blue}{m}\)

Answer 3

in this case: \(x_1=8\) and \(y_2=3\)

The slope is \(\rm m\)

Answer 4

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

Answer 5

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

Answer 6

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. $$\text{slope between }(x,y)\text{ and }(x_0,y_0)=m\\\frac{y-y_0}{x-x_0}=m\\y-y_0=m(x-x_0)$$

Answer 7

Yes B is correct! VEry good!

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

I'll attach the graphs.

Answer 14

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: $$y-y_0=m(x-x_0)\\y-y_0=mx-mx_0\\y=\color{blue}mx+\underbrace{\color{red}{y_0-mx_0}}_{b}\\y=mx+b$$

Answer 15

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

Answer 16

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).

Answer 17

y+5=2(x-4)

1. expand the left side)
2. subtract 5 from both sides

Answer 18

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

Answer 19

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

Answer 20

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.

Answer 21

(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.)

Answer 22

Possibly B?

Answer 23

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

Answer 24

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

Answer 25

yes

Answer 26

A is Correct

Answer 27

Do you have time to help with a few more?

Answer 28

(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)

Answer 29

yes, I think so...

Answer 30

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)

Answer 31

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)

Answer 32

Yes, your answer is right

Answer 33

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

Answer 34

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

Answer 35

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....

Answer 36

OH! Okay! So A would be correct.

Answer 37

Yup

Answer 38

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

Answer 39

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

Answer 40

Possibly D?

Answer 41

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)

Answer 42

-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?

Answer 43

C, I believe.

Answer 44

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

Answer 45

Then it must be D.

Answer 46

it is B