Please help me solve the following equation - This equation passes through (1,1) and (4,14)?

Question

is the answer a). 5x+6y=19 b). 5x-6=y c). -x+4y=15 d). 4x+5y= -1

please list the steps for solving this equation..
thank you

Answer 1

After several calculations, I have realized that you have probably given the wrong question, you might have missed out a negative sign or something. Since the choices for answers are already given, I will assume that this equation is linear(eg. takes the form of a line).

To find equation of a line, first obtain a gradient.

Gradient = (y1 - y2)/(x1 - x2)
= (14 - 1)/(4 - 1)
= 13/3

Since a linear equation takes the form of y = mx + c, your m is now 13/3. Thus, the equation looks something like this,

y = (13/3)x + c

The remaining variable c, can be found by substituting any of consequent values of x and y. Substituting the values for the point of (1,1), (ie. x = 4, y = 14)

14 = (13/3)(4) + c
14 - 52/3 = c
c = -10/3

Thus, the final equation will be,

y = (13/3)x - 10/3
3y = 13x - 10

This is the correct answer based on the question given. But it does not fit into any of the choices. Please get back to us on this.

Answer 2

First, find the slope for points (1,1) and (4,14)
m(slope) = (y2 – y1) / (x2 – x1) = (14 – 1) / (4 – 1) = 13/3

Second, find slope for other four equations: Y = mx +b
5x + 6y = 19
6y = -5x + 19
y = -5/6 + 19/6
m = -5/6

5x – 6 = y
y = 5x – 5
m = 5

-x + 4y = 15
4y = x + 15
y = ¼*x + 15/4
m = ¼

4x + 5y = -1
5y = -4x -1
y = -4/5*x – 1/5
m = -4/5

Since none of the slope above match, we need to find the equation by formula y – y1 = m(x – x1)
(we can pick points (1,1) or (4,14), but I rather do the easy one)
Y – 1 = 13/3 (x – 1)
Y – 1 = 13/3x – 13/3
Y = 13/3x – 13/3 + 1
Y = 13/3x – 10/3

Points (1, 4) and (4, 14) has the equation of y = 13/3x – 10/3

Answer 3

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

So slope equals:

(14-1) / (4-1) = 13/3

The equation of a line is: y = mx+b, where m is slope.

So,

a) 5x + 6y = 19
6y = -5x + 19

You can stop here since the slope is negative, and we know ours is positive.

b) This could be a solution, since the slope is positive.

c) -x+4y = 15
4y = x+15
y = x + 15/4

This also has a positive slope--it needs further consideration.

d) 4x + 5y = -1
5y = -4x -1
y = -4/5x -1

The slope here is negative, so we know this is wrong.

Let's explore b and c a little more:

If (1,1) is truly a solution, then when we plug them into the equation, it will hold.

This doesn't hold for any solution a-d.

Are you sure the points are correct?

Regards,

Mysstere

Answer 4

(1,1), (4,14)

Start off with the formula
y2-y1
x2-x1
equals m (slope)

14-1 = 13
//4-1 = 3
13/3 = m = slope

Then using the slope, use the formula y-y1=m(x-x1)
y-1=13/3(x-1)
y-1=13/3x-13/3
y=13/3x-10/3

"y = 13/3x - 10/3" is your equation
Seeing all your answer choices are in Standard Equation form, you have to change "y = 13/3x - 10/3" into Standard Form.

y=13/3x-10/3
-13/3x+y=10/3
Multiply both sides by "3"
-13x+3y=10

Well, um now I'm stuck. This is the only equation I come up with with the information you provided. None of those answer choices are valid. Even checking their slopes, they aren't even parallel to the line that passes through (1,1) and (4,14).

Check your answer choices or your points. Your welcome anyways.

Answer 5

of direction, in basic terms go multiplication outcomes in the respond, yet once you realize here, the line to the respond will become clearer. 6 / 11 = (6 * a) / (11 * a). that's, you may multiply the two facets with the comparable selection (some fee a), and the linked fee remains the comparable. So, for 6 / 11 and 114 / n to be the comparable, we could like 114 to be written in the kind 6 * a. of course, a = 114 / 6 = 19. of course, 6 / 11 = (6 * 19) / (11 * 19), so n = 11 * 19 = 209

Answer 6

First of, you will want to bring y to the left hand side of the equation, and all other stuff to the right, so that it looks like : Y=aX + C
let X=1, find Y,
let X=4, find Y again.
OR
find the gradient, which will give you the a in Y=aX + C
gradient for (x1,y1) and (x2,y2)
is (y2-y1) divided by (x2-x1).

Answer 7

The equation passes through two points.

Steps:

1. Find the slope of the given two points.

2. Once you find the slope, plug the slope and one of your given points (you select which one) into the point-slope formula.

This is all you need to do to find the equation that passes through ANY two points.

Guido

Answer 8

Steps to solve the problem:

1. Go to class, take notes
2. Read your book. Whatever class you're in, the book probably has a pretty good description of exactly how to do this problem, either that or enough that you shouldn't have a problem.