Question

A line passes through the points (10, 9) and has a slope of 5/2 write an equation in Ax+By=C

Answer 1

Answer:

5x - 2y = 32

Step-by-step 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:

`y-y_1=m(x-x_1)`

Substitute x₁ = 10, y₁ = 9, and m = 5/2 into the equation above

`\begin{gathered} y\text{ - 9 = }(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}`

5x - 2y = 32 is in the form Ax + By = C

where A = 5, b = -2, C = 32