ANSWER:
[tex]y=-\frac{5}{4}x+12[/tex]
STEP-BY-STEP EXPLANATION:
We can calculate the equation of the line, with the help of the two blue dots.
The first thing is to identify that the points are (4,7) and (8,2).
The equation of a line in its slope and intercept form is as follows:
[tex]\begin{gathered} y=mx+b \\ \text{ where m is the slope and b is y-intercept} \end{gathered}[/tex]
We calculate the slope as follows:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{ Replacing:} \\ m=\frac{2-7}{8-4}=-\frac{5}{4} \end{gathered}[/tex]
Now, the y-intercept is calculated as follows:
[tex]\begin{gathered} 2=8\cdot-\frac{5}{4}+b \\ 2=-10+b \\ b=2+10 \\ b=12 \end{gathered}[/tex]
Therefore the equation would be:
[tex]y=-\frac{5}{4}x+12[/tex]
