Question

The ordered pairs (0, 1), (3, 4) and (4, n) are solutions of the same linear equation. Find n.n =

Answer 1

In order to find the value of n, use the first two points (0,1) and (3,4) to find the line equation.

Use the following general formula for the equation of a line:

y - yo = m(x - xo)

where m is the slope of the line and (xo,yo) is any point in the line.

slope m is given by:

`m=(y_2-y_2)/(x_2-x_1)`

(x1,y1) and (x2,y2) are any pair of point on the line. For instance:

(x1,y1) = (0,1)

(x2,y2) = (3,4)

Replace the previous values into the formula for m:

`m=(4-1)/(3-0)=(3)/(3)=1`

Now, use (xo,yo) = (0,1) and replace these values into the general formula for a line, then, solve for y, as follow:

y - 1 = (1)(x - 0)

y - 1 = x

y = x + 1

The previous equation is the line which passes through the given points.

The value of n in the point (4,n) is the y coordinate of the point, which is the same that it is the value of y when x = 4. Then, by replacing x = 4, you have:

y = 4 + 1 = 5 = n

Hence, the value of n is n = 5