Question

Write an equation of the line that passes through the given points: (9/2,1), (-7/2,7) please show step by step how to do this. The answer should be: y=-3/4x+35/8.

Answer 1

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 ...

  $y=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)+y_1$

Filling in your given points, the equation becomes ...

  $y=\dfrac{7-1}{\frac{-7}{2}-\frac{9}{2}}(x-\frac{9}{2})+1$

After you fill in the values, it is a matter of simplifying the resulting equation.

$y=\dfrac{6}{\frac{-16}{2}}(x-\frac{9}{2})+1=\dfrac{-12}{16}(x-\frac{9}{2})+1=-\dfrac{3}{4}x+\left(\dfrac{-3}{4}\cdot\dfrac{-9}{2}\right)+1\\\\y=-\dfrac{3}{4}x+\dfrac{27+8}{8}\\\\y=-\dfrac{3}{4}x+\dfrac{35}{8}$