Given:
The points of the line are (4,4) and (5,7).
The objecive is to find the slope of the line.
Explanation:
Consider the given points as,
[tex]\begin{gathered} (x_1,y_1)=(4,4) \\ (x_2,y_2)=(5,7) \end{gathered}[/tex]The general formula to find the equation of line using two points is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Substitution:
Now, substitute the given values in the equation of striaght line.
[tex]\begin{gathered} y-4=\frac{7-4}{5-4}(x-4) \\ y-4=\frac{3}{1}(x-4) \\ y-4=3x-12 \\ y=3x-12+4 \\ y=3x-8 \end{gathered}[/tex]Thus, the equation obtained is y = 3x - 8.
Hence, it can be written in function notation as, f (x) = 3x - 8.
