The equation of a line in slope-intercept form, is:
[tex]y=mx+b[/tex]
Where m is the slope of the line and b is the y-intercept.
Notice that the trend line passes through the two yellow points, whose coordinates are:
[tex]\begin{gathered} (0,8) \\ (7,3) \end{gathered}[/tex]
Since the y-intercept is the value at which the line crosses the Y-axis, and we can see that the line crosses the Y-axis precisely at the point (0,8), then the value of the y-intercept is 8. This means that b=8.
On the other hand, the value of the slope can be found using the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Replace the coordinates of the points into the slope formula:
[tex]m=\frac{8-3}{0-7}=\frac{5}{-7}=-\frac{5}{7}[/tex]
Finally, replace m=-5/7 and b=8 to find the equation of the line in slope-intercept form:
[tex]y=-\frac{5}{7}x+8[/tex]
Therefore, the answer is:
[tex]y=-\frac{5}{7}x+8[/tex]
