Question

Write an equation for the line that has a slope of 1/2 and passes through the point (2,4)!!

Answer 1

x-2y=-6.

Step-by-step explanation:

Given a line with a slope of 1/2 that passes through the point (2,4):

`\begin{gathered} m=(1)/(2) \\ (x_1,y_1)=(2,4) \end{gathered}`

Substitute these into the point-slope form of the equation of a line:

`y-y_1=m(x-x_1)`

This gives:

`\begin{gathered} y-4=(1)/(2)(x-2) \\ y-4=(1)/(2)x-(1)/(2)(2) \\ y-4=(1)/(2)x-1 \end{gathered}`

We can simplify further:

`\begin{gathered} y=(1)/(2)x-1+4 \\ y=(1)/(2)x+3 \\ \implies y=(x+6)/(2) \\ 2y=x+6 \\ x-2y=-6 \end{gathered}`

The equation of the line is x-2y=-6.