<u>Given</u>:
We need to determine the equation of the line using the slope - intercept form.
(14) <u>Equation of the line:</u>
The slope of the line is
and the y - intercept is ![b=9](https://tex.z-dn.net/?f=b%3D9)
The equation of the line can be determined using the formula,
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Substituting the values, we get;
![y=-\frac{2}{3}x+9](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B2%7D%7B3%7Dx%2B9)
Therefore, the equation of the line is ![y=-\frac{2}{3}x+9](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B2%7D%7B3%7Dx%2B9)
(15) <u>Equation of the line:</u>
The slope of the line is
and the point (2,-9)
The equation of the line can be determined using the formula,
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
Substituting the values, we get;
![y+9=3(x-2)](https://tex.z-dn.net/?f=y%2B9%3D3%28x-2%29)
![y+9=3x-6](https://tex.z-dn.net/?f=y%2B9%3D3x-6)
![y=3x-15](https://tex.z-dn.net/?f=y%3D3x-15)
Thus, the equation of the line is ![y=3x-15](https://tex.z-dn.net/?f=y%3D3x-15)
(16) <u>Equation of the line:</u>
The two points of the line are (9,8) and (-6,-2)
The slope of the line is given by
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![m=\frac{-2-8}{-6-9}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-2-8%7D%7B-6-9%7D)
![m=\frac{-10}{-15}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-10%7D%7B-15%7D)
![m=\frac{2}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B2%7D%7B3%7D)
The equation of the line can be determined using the formula,
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
Substituting the values, we get;
![y-8=\frac{2}{3}(x-9)](https://tex.z-dn.net/?f=y-8%3D%5Cfrac%7B2%7D%7B3%7D%28x-9%29)
![y-8=\frac{2}{3}x-6](https://tex.z-dn.net/?f=y-8%3D%5Cfrac%7B2%7D%7B3%7Dx-6)
![y=\frac{2}{3}x+2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2%7D%7B3%7Dx%2B2)
Thus, the equation of the line is ![y=\frac{2}{3}x+2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2%7D%7B3%7Dx%2B2)