Question

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

Answer 1

Answer:

x-2y=-6.

Explanation:

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

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

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

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

This gives:

$\begin{gathered} y-4=\frac{1}{2}(x-2) \\ y-4=\frac{1}{2}x-\frac{1}{2}(2) \\ y-4=\frac{1}{2}x-1 \end{gathered}$

We can simplify further:

$\begin{gathered} y=\frac{1}{2}x-1+4 \\ y=\frac{1}{2}x+3 \\ \implies y=\frac{x+6}{2} \\ 2y=x+6 \\ x-2y=-6 \end{gathered}$

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