For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
According to the data given we have:
[tex]m = \frac {4} {3}[/tex]
Thus, the equation is of the form:
[tex]y = \frac {4} {3} x + b[/tex]
We substitute the given point and find the cut point "b":
[tex](x, y) :( 2,5)[/tex]
So:
[tex]5 = \frac {4} {3} (2) + b\\5 = \frac {8} {3} + b\\5- \frac {8} {3} = b\\b = \frac {3 * 5-8} {3}\\b = \frac {15-8} {3}\\b = \frac {7} {3}[/tex]
Thus, the equation is:
[tex]y = \frac {4} {3} x + \frac {7} {3}[/tex]
Finally, we have that the function is of the form[tex]y = f (x)[/tex], where [tex]f (x) = \frac {4} {3} x + \frac {7} {3}[/tex]
ANswer:
The function that describes the line is:[tex]f (x) = \frac {4} {3} x + \frac {7} {3}[/tex]
