From the image given, we can read the y-intercept, calculate the slope, and derive the equation of the line as follows:
- y-intercept = c = -2 (since the graph intercepts the y axis at -2)
- slope:
[tex]\text{slope}=m=\frac{y_2-y_1}{x_2-x_1}[/tex]
consider the points: (x1, y1) = (0, -2) and (x2, y2) = (-3, -1)
Thus:
[tex]\begin{gathered} \text{slope}=m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1_{}-(-2)}{(-3)_{}-0_{}}=\frac{-1+2}{-3-0}=\frac{1}{-3} \\ \Rightarrow\text{slope}=m=-\frac{1}{3} \end{gathered}[/tex]
- Now, the equation of the line is:
[tex]y=mx+c[/tex]
Thus:
[tex]y=-\frac{1}{3}x+(-2)[/tex][tex]\Rightarrow y=-\frac{1}{3}x-2[/tex]
