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

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-6)}{4-0}$

which gives

$m=\frac{6}{4}=\frac{3}{2}$

So, the line equation has the form

$y=mx+b\longrightarrow y=\frac{3}{2}x+b$

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

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

Then, the line equation is

$y=\frac{3}{2}x-6$

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