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Question

What is equation of the line between the points (16,5) and (4,8)?

Answer 1

The equation of a line is y-y1 = m(x-x1)

The equation of m is (y2 - y1) / (x2 - x1)

So m = (8-5)/(4-16) = 3/-12 = -1/4

Now you can use either point to get the line.

y - 5 = (-1/4)(x - 16)
y-5 = -x/4 + 4

y = -x/4 + 9

Answer 2

One way of doing it:
First determine the slope. This is the ratio of the horizontal and vertical differences of the points. It's probably spelled out real nicely in a box in your... textbook.

We would have:
(5 - 8)/(16 - 4),
( -3 )/( 12 ),
-1/4.

The slope is negative one-fourth, so the equation will look a little like:
y = -1/4 x + b.
'b' is where the line crosses the y-axis. You know that the equation holds for the points (16,5) and (4,8), so pick one.
Take (4,8): x=4 and y=8,
So 8 = -1/4 * 4 + b,
8 = -1 + b,
9 = b.

Hence our equation is
y = -1/4 x + 9.

Feel free to email me for further clarifications.

Answer 3

First find the slope m = (5-8)/16-4 = -3/12 = -1/4 Now find the y intercept by using either point along with the slope in the point slope form of the equation. I'll use the point (4,8) since it's easier. (-1/4)(x-4) = y-8 which is -1/4x + 1 = y - 8 = -1/4x + 9 = y. Finally, check to make sure that this equation generates the other point. (-1/4)(16) + 9 = -4 + 9 = 5. voila!

Answer 4

First: find the slope:

m = (second y - first y)/(second x - first x)
*take the numbers and place them in the formula:

m = (8-5)/(4-16)
m = 3/-12 and simplify to (-1/4)

Second: plug a set of points and the slope into the slope-intercept form to find the y-intercept known as "b."

y = mx+b
*Let's use: (4,8); m = -1/4

8 = (-1/4)(4) + b
8 = -1 + b
8 + 1 = -1+1 + b
9 = b; b = 9

Fourth: take the slope and y-intercept and place them into the slope-intercept formula:

y = (-1/4)x + 9 Or y = -x/4 + 9

Answer 5

Ok. Hello!

(16,5) and (4,8) in slope-intercept form:

The formula is: y = Mx + B

To find the slope of these two points formula: 8 - 5 over 4 - 16
Equals: 4 over -12
Simplify the slope: -3

Ok, now that you have the slope, plug it in for M.
y = -3x + b

And then choose a coordinate: [4,8]
and plug it in.
The 4 is X and 8 is Y:

8 = -3[4] + b

Now it's simple algebra:
8 = -12 + b
10 = b

now that you have everything:
y = -3x + 10

....You know that "M" stands for slope and "B" stands for the y-intercept. So you plug your answers in....

Your answer is: y = -3x + 10


I HOPE THAT HELPED! I CARE AND I TRY! <=D

Answer 6

slope=(5-8)/(16-4)=-3/12=-1/4
y=-x/4+b
8=14/4+b
9=b
y=-x/4+9 in slope intercept form

x+4y=36 in standard form.

Answer 7

y-y1/y2-y1=x-x1/x2-x1
=(y-5)/(8-5)=(x-16)/(4-16)
-12(y-5)=3(x-16)
-12y+60=3x-48
adding -3x+48
3x-12y+12=0
dividing by 3
x-4y+4=0