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

Step-by-step 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=(y_2-y_1)/(x_2-x_1)(x-x_1)+y_1`

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

`y=(7-1)/((-7)/(2)-(9)/(2))(x-(9)/(2))+1`

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

`y=(6)/((-16)/(2))(x-(9)/(2))+1=(-12)/(16)(x-(9)/(2))+1=-(3)/(4)x+\left((-3)/(4)\cdot(-9)/(2)\right)+1\\\\y=-(3)/(4)x+(27+8)/(8)\\\\y=-(3)/(4)x+(35)/(8)`