The slope of line g is 9/4.
<u>Step-by-step explanation:</u>
The line f passes through points (1,14) and (10,10).
Line g is perpendicular to f.
<u>To find the slope of line f :</u>
The formula for slope is given by,
![Slope = (y2-y2)/(x2-x1)](https://tex.z-dn.net/?f=Slope%20%3D%20%28y2-y2%29%2F%28x2-x1%29)
Here, The point (1,14) is (x1.y1) and (10,10) is (x2,y2).
⇒ ![(10-14) / (10-1)](https://tex.z-dn.net/?f=%2810-14%29%20%2F%20%2810-1%29)
⇒ ![-4 / 9](https://tex.z-dn.net/?f=-4%20%2F%209)
Therefore, the slope of line f is -4/9.
<u>To find the slope of line g :</u>
Since, the line g is perpendicular to f, the slope of g will be the negative reciprocal of slope of line f.
⇒ slope of g = - (1 / slope of f).
⇒ ![- (1 / (-4/9))](https://tex.z-dn.net/?f=-%20%281%20%2F%20%28-4%2F9%29%29)
⇒ ![9/4](https://tex.z-dn.net/?f=9%2F4)
∴ The slope of line g is 9/4.