Question

pls help with both the equationsFind the equation satisfying the given set of points.(Here the first row represents the x-values while the second row represents y-values.

Answer 1

In the question, various values of inputs (x) are given along with their corresponding outputs (y).

Observe the output values carefully. You will observe that the increase in two consecutive values is constant. It means the change is linear.

So the points will form the equation of a line.

Consider the two point form of a straight line,

`y-y_1=\frac{y_2-y_1}{x_2-x_1_{}}.(x-x_(1))`

Consider the first two points (1,6) and (2,7),

`y-6=\frac{7_{}-6}{2-1}.(x-1)\Rightarrow y-6=1(x-1)\Rightarrow x-y+5=0_{}`

Thus, the equation of the line is obtained.

You can check if the equation is correct if it satisfies the other two points also.

Check for the point (3,8),

`3-8+5=-5+5=0`

It means point (3,8) satisfies the equation.

Check for the point (4,9),

`4-9+5=-5+5=0`

It means point (4,9) satisfies the equation.

Thus, the equation obtained is valid and correct for the given points.