Question

For #1-4 write the equation of the line in slope-intercept form.

Answer 1

We have to write the equations of the line in the slope intercept form:

`y=mx+b`

1. In the graph we see that the y-intercept (the value of the line when x=0) is y=3. Then, we already know the value of b (b=3).

Using the other known point (3,0), we can calculate the slope m:

`\begin{gathered} y=mx+3 \\ 0=m\cdot(3)+3 \\ 0=3m+3 \\ m=-(3)/(3) \\ m=-1 \end{gathered}`

Then, with m=-1 and b=3, we can write the equation as:

`y=-x+3`

2. In this case, the line is defined only for x=-4. The slope and the y-intercept tend to infinity. So the only equation to represent this line is x=-4.

3. We see that the y-intercept is y(0)=-2. Then, b=-2.

We use the point (1,0) to calculate the slope m:

`\begin{gathered} y=mx-2 \\ 0=m\cdot1-2 \\ 0=m-2 \\ m=2 \end{gathered}`

Then, with m=2 and b=-2, we can write the equation as:

`y=2x-2`

4. In this case, the line is defined only for y=-2. This is the y-intercept (b=-2), while the slope, as the line does not change value in function of x, is 0.

Then, with m=0 and b=-2, the equation is:

`y=-2`