Question

can you please solve this practice problem for me I really need assistance .The original line is the one without dots.

Answer 1

A line can be written with the equation:

`y=mx+b`

Where m is the slope and b is the y-intercept.

Lines that are paralle have the same slope, m, and different values for b.

So, if we get the graph for one line, we can:

- find the slope of the original line

- the slope of the paralle line is the same, so we also found it already.

- choose a point of b that gives a line different from the one before.

Let (x₁, y₁) and (x₂, y₂) be points on the original line. Thus, the slope m will be:

`m=(y_2-y_1)/(x_2-x_1)`

From the graph of the original line, we can choose these 2 points. Let's choose these:

Which are (0, -5) and (-3, 1). Using them into the formula, we have:

`m=(1-(-5))/(-3-0)=(1+5)/(-3)=(6)/(-3)=-2`

So, the slope of the original line is -2 and (0, -5) is the y-intercept, so b = -5 and the equation of the line is:

`y=-2x-5`

Now, the slope of the parallel line is the same, so the slope of the parallel line is -2.

Since we can choose any parallel line to draw (different from the given one), we can choose the simplest one, which will have b = 0 and equation:

`y=-2x`

So, we can get two points in it:

x = 0:

`\begin{gathered} y=-2\cdot0 \\ y=0 \end{gathered}`

And x = -3:

`\begin{gathered} y=-2\cdot(-3) \\ y=6 \end{gathered}`

So, the graph will be: