Explanation:
The easiest way to do this is to make use of the 2-point form of the equation for a line. For points (x₁, y₁) and (x₂, y₂), the equation is ...
[tex]y=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)+y_1[/tex]
Filling in your given points, the equation becomes ...
[tex]y=\dfrac{7-1}{\frac{-7}{2}-\frac{9}{2}}(x-\frac{9}{2})+1[/tex]
After you fill in the values, it is a matter of simplifying the resulting equation.
[tex]y=\dfrac{6}{\frac{-16}{2}}(x-\frac{9}{2})+1=\dfrac{-12}{16}(x-\frac{9}{2})+1=-\dfrac{3}{4}x+\left(\dfrac{-3}{4}\cdot\dfrac{-9}{2}\right)+1\\\\y=-\dfrac{3}{4}x+\dfrac{27+8}{8}\\\\y=-\dfrac{3}{4}x+\dfrac{35}{8}[/tex]
