Question

Find the equation of the line that passes through (4.4) and (5,7). Use function notation.

Answer 1

Given:

The points of the line are (4,4) and (5,7).

The objecive is to find the slope of the line.

Step-by-step explanation:

Consider the given points as,

`\begin{gathered} (x_1,y_1)=(4,4) \\ (x_2,y_2)=(5,7) \end{gathered}`

The general formula to find the equation of line using two points is,

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Substitution:

Now, substitute the given values in the equation of striaght line.

`\begin{gathered} y-4=(7-4)/(5-4)(x-4) \\ y-4=(3)/(1)(x-4) \\ y-4=3x-12 \\ y=3x-12+4 \\ y=3x-8 \end{gathered}`

Thus, the equation obtained is y = 3x - 8.

Hence, it can be written in function notation as, f (x) = 3x - 8.