Question

What is the equation of the line that goes through the points (4,5) and (8,-3)

Answer 1

To calculate the equation of a line passing through two points, we use the formula;

`\begin{gathered} (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \\ \text{where (x}_1,y_1)=(4,5)and(x_2,y_2)\text{ = (8, -3)} \\ \text{Putting these values in the formula we have;} \\ (y-5)/(x-4)=(-3-5)/(8-4) \\ (y-5)/(x-4)=(-8)/(2) \\ (y-5)/(x-4)=(-4)/(1) \end{gathered}`
`\begin{gathered} \text{Cross multiplying, we have} \\ y-5=\text{ -4(x-4)} \\ y-5=-4x+16 \\ y=-4x+16+5 \\ y=-4x+21 \end{gathered}`

Therefore the equation of the line is y = -4x + 21