Question

(0, 5) and (-5, 1) what is the linear equation for the two given points

Answer 1

`\begin{gathered} \text{ The equation of a line that passes trough two points (x1,y1) and (x2,y2) is} \\ y=mx+b \\ \text{where} \\ m=(y_2-y_1)/(x_2-x_1) \end{gathered}`
`\begin{gathered} \text{thus } \\ m=(1-5)/(-5-0) \\ m=(-4)/(-5) \\ m=(4)/(5) \end{gathered}`
`\begin{gathered} \text{ the equation is now} \\ y=(4)/(5)x+b \\ \text{now, if we replace the point (0,5) x=0, y=5, then the value of b is} \\ 5=(4)/(5)(0)+b \\ 5=0+b \\ 5=b \\ \\ \text{and the equation is now} \\ y=(4)/(5)x+5 \end{gathered}`