Question

Draw a graph of each of the following lines on the grid below. label each with its equation

Answer 1

A = first equation, B = second equation, C = third equation, D = fourth equation.

on the graph.

Step-by-step explanation:

Given the equations;

`y=x+5`
`y=-(5)/(2)x+9`
`y=(2)/(3)x-6`
`y=-x-2`

We want to graph the equations on the grid.

To graph the linear equations, let us derive two points on each of the equations so that we can plot them on the grid.

For the first equation;

`\begin{gathered} y=x+5 \\ at\text{ x=0;} \\ y=0+5=5 \\ (0,5) \\ \\ at\text{ x=4;} \\ y=4+5 \\ y=9 \\ (4,9) \end{gathered}`

For the second equation;

`\begin{gathered} y=-(5)/(2)x+9 \\ at\text{ x=0;} \\ y=-(5)/(2)(0)+9 \\ y=9 \\ (0,9) \\ \\ at\text{ x=4;} \\ y=-(5)/(2)(4)+9 \\ y=-10+9 \\ y=-1 \\ (4,-1) \end{gathered}`

For the third equation;

`\begin{gathered} y=(2)/(3)x-6 \\ at\text{ x=0;} \\ y=(2)/(3)(0)-6 \\ y=-6 \\ (0,-6) \\ \\ at\text{ x=6;} \\ y=(2)/(3)(6)-6 \\ y=4-6 \\ y=-2 \\ (6,-2) \end{gathered}`

For the fourth equation;

`\begin{gathered} y=-x-2 \\ at\text{ x=0;} \\ y=-0-2 \\ y=-2 \\ (0,-2) \\ \\ at\text{ x=4;} \\ y=-4-2 \\ y=-6 \\ (4,-6) \end{gathered}`

Since we now have the points on each equation, let us plot on the grid and join the points;

A = first equation, B = second equation, C = third equation, D = fourth equation.

on the graph.