Answer :
The answer is: y = - 150x + 8400
The two points are given in the (x, y) format. Meaning that
x1= 0 and y1 = 8400, while
x2 = 10 and y2 = 6900.
We are required to find the slope given two points (0, 8400) and (10, 6900).
This is easily done if we use the slope formula.
The slope formula is given below:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\text{Slope} \end{gathered}[/tex]Now we can proceed to finding the slope:
[tex]\begin{gathered} m=\frac{6900-8400}{10-0}=-\frac{1500}{10} \\ \\ \therefore m=-150 \end{gathered}[/tex]Now that we have the slope (m), we can also find the intercept (b) using the equation given in the question:
[tex]y=mx+b[/tex]Here we shall use any of the coordinates: (10, 6900) or (0, 8400)
Using (10, 6900) implies: x = 10 and y = 6900
Substituting these values into the equation above:
[tex]\begin{gathered} y=mx+b \\ y=6900, \\ x=10 \\ m=-150 \\ \\ 6900=-150\times10+b \\ 6900=-1500+b \\ \text{add 1500 to both sides} \\ \\ 6900+1500=-1500+1500+b \\ 8400=b \\ \therefore b=8400 \end{gathered}[/tex]Since we now have slope (m) and intercept (b), we can therefore write the equation as follows:
[tex]\begin{gathered} y=mx+b \\ m=-150 \\ b=8400 \\ \\ \therefore y=-150x+8400 \end{gathered}[/tex]The final answer is: y = - 150x + 8400