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=(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=(0-4)/(2-0)=-2`

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

`\begin{gathered} 4=0*-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=-(1)/(-1)=1 \\ -1=0*1+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=(-4-8)/(0+4)=-3 \\ -4=-3*0+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=(4-4)/(-4)=0 \\ 4=0+b \\ b=4 \\ y=0+4 \\ y=4 \end{gathered}`