Question

I need help with this please. Find the line equation.

Answer 1

We need to find the line equation. From the given picture, we can choose 2 points along the line, for instance,

`\begin{gathered} (x_1,y_1)=(0,-6) \\ (x_2,y_2)=(4,0) \end{gathered}`

The slope of the line is given by

`m=(y_2-y_1)/(x_2-x_1)=(0-(-6))/(4-0)`

which gives

`m=(6)/(4)=(3)/(2)`

So, the line equation has the form

`y=mx+b\longrightarrow y=(3)/(2)x+b`

We can find the y-intercept b by substituting the point (0,-6) into the last result, that is,

`\begin{gathered} -6=(3)/(2)(0)+b \\ \text{then} \\ b=-6 \end{gathered}`

Then, the line equation is

`y=(3)/(2)x-6`

Now, by multiplying both sides by 4, we get

`4y=6x-24`

By subtracting 6x to both sides, we have

`4y-6x=-24`

and by multiplying both sides by -1, we obtain

`6x-4y=24`

By comparing with the given options, the answer is the second option on the left hand side: 6x - 4y = 24