Question

Find an equation of the line through A (-6, 5) having slope 7

Answer 1

In the slope-intercept form, plug (x,y) in to find the equation.

Answer 2

General equation of a straight line.
Either y=mx+c or (y-y1)=m(x-x1)
Slope 7 therefore substitute 7 into the equation as m. Then put in x and y.

Answer 3

The slope-intercept being \[y=mx+b\]\[5=(7(-6)+b\]

Answer 4

but in this question only one point given?

Answer 5

Yes, but you have the slope.

Answer 6

You only need a point and a slope to find a straight line function.

Answer 7

so I use this formula for finding equation of line : y=mx+b? Or I can also use this one y-y1 = m (x-x1) ?

Answer 8

Either is acceptable, but you generally use the 1st if you've just started doing this sort of stuff.

Answer 9

E.g.: I have a function g
Its slope is 0 and passes by the origin



You plug everything in the equation to find the x-intercept
\[f(g)=mx+b\]\[0=0x+b\]\[b=0\]
\[f(g) = 0x + 0\]\[f(g)=x\]

The formula \[\large m= \frac{y_{2} - y_{1}}{x_{2}-x_{1}},~~m=slope\]
is usually used when you want to find the slope with 2 points given.

Answer 10

Thanks zepp I only just need to plug the values or do simplification in it?

Answer 11

Yes, what I did above is to find the y-intercept, you already have the slope.

Remember, a straight line function is defined by 2 things: the slope and the y-intercept

Answer 12

So I don't need more simplication, that's my answer ?

Answer 13

y=mx+b
5=7(-6)+b
?

Answer 14

Yes! ;D

Answer 15

The reason why you use y-y1 etc is because that is the totally general formula. You will notice sonner or later that y=mx+c does not work for vertical lines etc. Also it is easier to manipulate in some circumstances

Answer 16

Find 'b'

Answer 17

Thank you, and sorry my English is not good.

Answer 18

my contribution is this:

\[y-y_o=m(x-x_o)\]
\[y=y_o=mx-mx_o\]
\[y=mx-mx_o+y_o\]

\[y = mx+b; \ b=y_o-mx_o\]

Answer 19

got a spurious "=" in there

Answer 20

lol two equals

Answer 21

:)

the point is; you dont have to resolve for b, its already there

Answer 22

it means b = 7(-6) +5

Answer 23

and now if I solve it, I will find the interecpt ?

Answer 24

\[y=mx-mx_o+y_o\] \[y=7x-7(-6)+5\]

Answer 25

but y is given in this question?

Answer 26

xo and yo are given; not x and y

x and y are generic points for input and output of the equation itself

xo and yo are points to establish the equation with and are constant

Answer 27

Thought it would be lot easier with the method I showed? D:
\[y=mx+b\]\[5=7(-6)+b\]\[5=-42+b\]\[b = 5--42\]\[b=47\]

Then plug everything back
\[y=mx+b\]\[y =7(the slope)x + 48\]\[y=7x+47\]

Answer 28

got a spurious "8" in there

Answer 29

those 8s can be tricky

Answer 30

Thanks Zep, your procedure is simple compared to amistre but thank you both of you :)

Answer 31

No offence, @amistre64, just a joke :P

Np ;)