People, I forgot how to solve the following Math Problem, would you be able to help me please?

Question

I have a problem in Math that I have to solve because it is kind of a take-home quiz, and I am allowed to look for resources. Please, people, out there, help me solve it. I knew how, but I forgot.

A straight line with slope 5 contains the points (1,2) and (3,k). Find the value of K.

Please show your procedure of solving it to refresh my memory.

Thank you!!

Answer 1

y = m x + b

m = (y2 - y1) / (x2 - x1)

x1 = 1, y1 = 2
x2 = 3, y2 = k

5 = (k - 2) / (3 - 1)
5 = (k - 2) / 2
10 = k - 2
k = 12

Answer 2

There are many ways to do this one, but perhaps the easiest, fro an understanding perspecitve, is to rememebr that a straigh lien funciton looks like

y=m x + b

where "m" is the slope

Since you already know the slope is 5, you have

y=5 x + b

and given that you've been told one point is (1,2) (x=1, y=2), the plugging those in the equation to resolve for "b"is:

2 = 5 * 1 + b
2 = 5 + b
-3 = b

So the equation is

y = 5 x - 3

For x=3, you'd have

y = 5 * 3 - 3
y= 15 - 3
y = 12

So the value of "k" is 12.

And some claim math is hard...

Answer 3

1 = 4 3 = 58

Answer 4

Remember the slope point formula

y-y1=m(x-x1)

input the slope and the first coordinate for (x1,y1)
y-2=5(x-1)
simplify
y=5x-5+2

y=5x-3 --------- (1)

then do the same for the second set of coordinates

y-k=5(x-3)
y=5x-15+k --------------(2)

Solve by comparison: y=y so (1)=(2)
Then solve for k

5x-3=5x-15+k
5x-5x+15-3=k
k=12


Therefore k equals 12

Answer 5

Slope is defined as the change in y over the change in x, so the slope is (k-2)/(3-1), if the two points are (1,2) and (3,k). Since slope equals 5, and 3-1=2,
(k-2)/2=5

k-2=10
k=12

Answer 6

The slope of your line is 5 (or 5 / 1), meaning it goes up 5 units for every 1 unit it moves to the right.

If you start at (1, 2) and are moving two units to the right [to get an x-coordinate of 3], your line will move upward from 2 ten units to 12.

k = 12.

Answer 7

Standard equation of a line is (y-y1) = m(x-x1) with (x,y) being a point and (x1, y1) being another...and m is the slope of your line. So you will need to solve (2-k)=5(1-3)

2 - k= -10
2 + 10 = k
k = 12

Answer 8

the equation you use is (y2-y1)/(x2-x1) = slope so (k-2)/(3-1) = 5 solve for k. k=12 another way to figure this out is slope equals rise over run so if slope is 5/1 and you increase run by 2 then you increase rise by 10.

Answer 9

Slope:
(y2-y1)/(x2-x1)
(k-2)/(3-1)
k-2/2

10=k-2
k=12

Check:
(1,2)(3,12)
(12-2)/(3-1)
10/2=5

Answer 10

The equation is
y = 5x + b, and you need to find b.

sub x = 1, y = 2 and that will give you the value of b.

k is the value of y when x = 3, so having found b, sub x = 3 and you have the answer.