Writing the equation?

Question

Heres what I have to do:

Write the equation of the line that passes through point (-3,-5) and (3,0).

First I found the slope:

m = [0 - (-5)] / [3 - (-3)] = 5/6

I'm having trouble finding the y-intercept from the coordinates given. Help is much appreciated! Thanks in advance : )

Ah, ok.. so I just had to plug in one of the set of coordinates. Alrighty, thanks all! : )

Answer 1

Ok, given the points (-3,-5) and (3,0)

The slope is correct, rewriting

m=(0-(-5))/(3-(-3))=5/6

so we have y=(5/6)x +b , and we need to find b. b is the y-intercept.

Put either point in the equation and solve for b, both of them must work!

(3,0) : 0=(5/6)(3)+b , b=-5/2

(-3,-5): -5=(5/6)(-3)+b , -5=(-5/2) +b, again b=-5/2

Hope this helps!

Answer 2

To find the y-intercept, use the formula:

y = mx + b

b = y - mx

So choose one of the 2 points given and plug their values into the equation. So using (3,0):

b = 0 - 5/6(3)

b = -5/2

So from here, it's easy to figure out the equation of the line. If you need further help, it is

y = 5/6x - 5/2

if your teacher doesn't like fractions, you can simplify by multiplying both sides by 6 to get

6y = 5x - 15

Answer 3

Write
y=mx+b
you know m and you can use either point in the equation to get b:

0=m*3+b
b=-3m=-3(5/6)=-5/2

therefore,
y=5x/6 -5/2

It's good to check the answer
for point 1
-5 =? 5(-3)/6-5/2 = -15/6-15/6 = -30/6 = -5 OK, it checks.

Answer 4

Here's the next step:
(y-y1)=m(x-x1)
y-(-5)=5/6(x-(-3))
y+5=5/6(x+3)
y+5=5/6x+15/6
y=5/6x+5/2-10/2
y=5/6x-5/2

Answer 5

Since you have the slope use the slope intercept form:

y=mx+b

Plug in 5/6 as the slope, then plug in one of the points and solve for b.

Then put the pieces together and get your equation.

Answer 6

y = mx + c

take one of the given values of (x,y). we take (3,0)

then, c = y - mx = 0 - 5/6*3 = - 5/2

y-intercept = - 5/2

Answer 7

y = mx + b

Substitute, using your calculated m, and solve for b:

-5 = (5/6) (-3) + b
-5= -15/6 + b
-2.5= b

or

0= 5/6 (3) + b
0= 15/6 + b
-2.5 = b

so it checks out.
Done.

Answer 8

This is the formula to write the equation for the above points :
y - y1 / x - x1 = y2 - y1 / x2 - x1

Answer 9

m=(-5-0)/(-3-3)=-5/(-6)=5/6

y=5x/6+b
0=5*3/6+b
-5/2=b
b=-5/2
y=5x/6-5/2

check
-5=5(-3)/6-5/2
-5=-5/2-5/2=-10/2=-5