Question

I've been really struggling with this question can I get a little help?

Answer 1

The line equation in its general form for a point (x, y) can be written as,

$\begin{gathered} y=mx+b \\ m\rightarrow slope=\frac{y2-y1}{x2-x1} \end{gathered}$

and b is the y intercept.

Let us first consider, the line m, and take the points on it, (0, 4) and (2, 0)

Therefore, slope can be calculated as,

$m=\frac{0-4}{2-0}=-2$

Taking the points (0, 4), b can be calculated as,

$\begin{gathered} 4=0\times-2+b \\ b=4 \end{gathered}$

Thus, the equation is,

$y=-2x+4$

Now, let us take the line, n and points, (1, 0) and (0, -1),

$\begin{gathered} m=-\frac{1}{-1}=1 \\ -1=0\times1+b \\ b\text{ = -1} \end{gathered}$

Therefore the equation is,

$y\text{ =1x-1}$

Letus now take the line p, and the points, (-4, 8) and (0, -4)

$\begin{gathered} m=\frac{-4-8}{0+4}=-3 \\ -4=-3\times0+b \\ b=-4 \\ \rightarrow y=-3x-4 \end{gathered}$

Now, taking the line l, we have the points, (0, 4) and (-4, 4)

$\begin{gathered} m=\frac{4-4}{-4}=0 \\ 4=0+b \\ b=4 \\ y=0+4 \\ y=4 \end{gathered}$