Question

what is the equation of the blue line

Answer 1

Answer:

The blue line is the translate in the direction of the red line by , and therefore has equation y = 3 ( x − 4 ) + 5 or y = 3 x − 7 .

Answer 2

Answer:

x - 2y + 4 = 0

Step-by-step explanation:

To find:- Equation of the blue line in the graph.

Solution:-

We know that, equation of a straight line is y = mx + c.

In the given figure, the blue line is passing through the co-ordinates (2, 3), (4, 4), (6, 5), (8, 6), (10, 7).

The two point formula for finding equation of a straight line is

                                  $\frac{y - y_{1} }{y_{2} - y_{1} } = \frac{x - x_{1} }{x_{2} - x_{1} }$

Let's take any two point $(x_{1}, y_{1} )$ = (6, 5) and $(x_{2}, y_{2} )$ = (10, 7)

Putting these two points in the above formula

(y - 5)/(7 - 5) = (x - 6)/(10 - 6)

⇒ (y - 5)/2 = (x - 6)/4

⇒ 4(y - 5) = 2(x - 6)

⇒ 2(y - 5) = x - 6

⇒ 2y - 10 = x - 6

⇒ x - 6 - 2y + 10 = 0

⇒ x - 2y + 4 = 0

Therefore, equation of the blue line in the figure is x - 2y + 4 = 0.

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