Hello!
The answer is:
The correct option is the first option,
[tex]y=\frac{5}{4} (x-1)[/tex]
Why?
To solve this problem, we need to remember that the point-slope form of a line is given by the following equation:
[tex]y-y_{1}=m(x-x_{1})\\\\y-0=\frac{5}{4}(x-1)[/tex]
We are given two points of the line,
[tex](5,5)\\(1,0)[/tex]
Where,
[tex]x=5\\x_{1}=1\\y=5\\y_{1}=0\\[/tex]
Then, substituting the given points into the equation ,to calculate m (slope), we have:
[tex]m=\frac{y-y_{1}}{x-x_{1}}[/tex]
[tex]m=\frac{5-0}{5-1}=\frac{5}{4}[/tex]
The slope of the function is [tex]\frac{5}{4}[/tex]
Now, substituting "x1" and "y1" and the slope in the point-slope equation, we have:
[tex](y-0)=\frac{5}{4} (x-1)[/tex]
[tex]y=\frac{5}{4} (x-1)[/tex]
Hence, the correct option is the first option,
[tex]y=\frac{5}{4} (x-1)[/tex]
Have a nice day!
