Question

Write an equation for the line graphed belowFrom the graph, you can see that (0,-1) and (1,-3) are two points on this line.

Answer 1

We can see the graph of a line, and we have the following points: (0, -1) and (1, -3), and we need to find the equation of the line in slope-intercept form.

Then to find the equation, we can proceed as follows:

1. We have to apply the two-point equation of the line:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

2. Now, we can label both points as follows:

• (0, -1) ---> x1 = 0, y1 = -1

,

• (1, -3) ---> x2 = 1, y2 = -3

3. We can substitute these values into the two-point form of the line:

$\begin{gathered} y-(-1)=\frac{-3-(-1)}{1-0}(x-0) \\ \\ y+1=\frac{-3+1}{1}(x)=-2x \\ \\ y+1=-2x \end{gathered}$

4. Finally, we have to subtract 1 from both sides of the equation:

$\begin{gathered} y+1-1=-2x-1 \\ \\ y=-2x-1 \end{gathered}$

Therefore, in summary, the equation of the line in slope-intercept form is:

$y=-2x-1$