5x - 2y = 32
Explanation:The line passes through the point (10, 9)
That is, x₁ = 10, y₁ = 9
The slope of the line, m = 5/2
The point-slope form of the equation of a line is:
[tex]y-y_1=m(x-x_1)[/tex]Substitute x₁ = 10, y₁ = 9, and m = 5/2 into the equation above
[tex]\begin{gathered} y\text{ - 9 = }\frac{5}{2}(x\text{ - 10)} \\ \text{Cross multiply} \\ 2(y\text{ - 9) = 5(x - 10)} \\ \text{Expand the equation} \\ 2y\text{ - 18 = 5x - 50} \\ 5x\text{ - 2y = -18 + 50} \\ 5x\text{ - 2y = }32 \end{gathered}[/tex]5x - 2y = 32 is in the form Ax + By = C
where A = 5, b = -2, C = 32