write the linear equation

Question

x     y

3     -5

6     -3

9     -1

12    1

Answer 1

Juliet just showed you the algebraic method.  I would like to show you the graphical method.

 

 

First plot the all the points on a coordinate system.  Then connect all these points.  Since the scale among the x values is consistent and the scale among the y values are also consistent, you should obtain a straight line throughout the entire coordinate system.  A straight line indicates that the function will be a linear type.  This means that the function will be in the form

 

y = mx + b  , as Juliet pointed out.

 

m = slope

b = y-intercept

 

Once you have drawn your line, count the number of vertical units and the number of horizontal units between consecutive points.  Divide the number of vertical units by the number of horizontal units.  This is your slope. Finally, scan your coordinate system to find the y value that has the x value of 0.  This y value is your y-intercept.

 

Plug in the slope and y-intercept, and you will have your linear equation. The equation will match Juliet's equation from the algebraic method.

 

Answer 2

Hi Latoya, I hope that the following will help you with the question. 

 

Concepts that you need to know: 

1) Linear equation is equation of a straight line, which is in the form of y = mx+c where m is the gradient and c is the y-intercept of the line.

2) Gradient of a straight line passing through two points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁).

 

Problem solving idea:

The given information tells you the four points that the line passes through. Just use ANY two points to find the unknowns m and c, then put the answer in the form of y = mx+c will do. I will use the points (3, -5) and (12, 1) as (x₁, y₁) and (x₂, y₂) respectively for the solution below. 

 

Solution:

m = (1 - (-5))/(12 - 3)

    = 6/9

    = 2/3

Now, y = mx + c gives y = (2/3)x + c.

*To find c, use ANY point on the line.

From the point (12, 1), when x = 12, y =1.

Together with y = (2/3)x + c, we have

1 = (2/3)(12) +c.

1 = 8 + c

c = -7

In conclusion, the linear equation is y = (2/3)x - 7.

 

Checking of solution:

You can check that your answer is correct by substituting the coordinates of the four points given into y = (2/3)x - 7.