Question

A graph of a linear equation passes through (-2,0) and (0,-6). 1. Use the two points to sketch the graph of the equation. 1 966 -5=4 1 2. 34 6 9 22 -4 5 a - 2 : 2005, Agnes Azzolino www.mathnstull.com/git9x9nolgir PermissDDESiDried The HOY puposes 2. Is 3x-y =- 6 an equation for this graph? Explain how you know.

Answer 1

1.

2.Yes , it is the equation of the line

Explanation

Step 1

locate the points on the plane

$\begin{gathered} LetA=(-2,0) \\ x\rightarrow-2 \\ y\rightarrow0 \end{gathered}$

and

$B=(0,6)$

B(red)

o for x(horizontally), and 6 for y(vertically)

Step 2

now, draw a line conecting the points

Step 3

2

Is 3x-y =- 6 an equation for this graph?

to prove this ,pick up a point of the line and replace the values for x and y, it must satisfies the equation

let

P(0,6)

so, replacing

$\begin{gathered} 3x-y=-6 \\ 3(0)-6=-6 \\ 0-6=-6 \\ -6=-6\rightarrow true \end{gathered}$

now, for other points

P(-2,0)

$\begin{gathered} 3x-y-6 \\ 3(-2)-0=6 \\ -6-0=-6 \\ -6=-6\rightarrow true \end{gathered}$

there is just one line that passes trhough those points, and both points fit the equations, so the answer is

Yes , it is the equation of the line

I hope this helps you