Answer:
[tex]y=-\frac{1}{3}x+4[/tex]From the graph, we can see that line AB passes through the points (-3, 5) and (3,3)
We know that the slope-intercept form of the equation of the lines goes by:
[tex]y=mx+b[/tex]Where:
m = slope
b = y-intercept
To get the slope, we are going to use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Again, with the points (-3, 5) and (3, 3), we will substitute the corresponding values to the formula
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{3-5}{3-(-3)} \\ m=\frac{-2}{6} \\ m=-\frac{1}{3} \end{gathered}[/tex]Now, we got a slope of -1/3. Next, we need to find the y-intercept (b). We are going to solve it by using the formula y = mx + b, while substituting the point (-3, 5) and the slope -1/3.
[tex]\begin{gathered} y=mx+b \\ 5=-\frac{1}{3}(-3)+b \\ 5=1+b \\ b=5-1 \\ b=4 \end{gathered}[/tex]We now have the value of our y-intercept. Since we now have both slope (m) and y-intercept (b), we will substitute both values to the slope-intercept form of the equation of the line to get the final answer.
[tex]\begin{gathered} y=mx+b \\ y=-\frac{1}{3}x+4 \end{gathered}[/tex]Therefore, the final answer is:
[tex]y=-\frac{1}{3}x+4[/tex]