Question

02 » Modules > Hawkes > Hawkes Single Sign OnQuestion 5 of 10, Step 1 of 14/15CorrectConstruct parametric equations describing the graph of the line passing through the following points.

Answer 1

The equation of a line passing through two given points is expressed as

`\begin{gathered} y-y_1=((y_2-y_1)/(x_2-x_1))(x-x_1)\text{ ----- equation 1} \\ where \\ (x_1,y_1)\text{ and \lparen x}_2,y_2)\text{ are the points through which the line passes} \end{gathered}`

Given that the line passes through the points (20,-14) and (12, -12), this implies that

`\begin{gathered} x_1=20 \\ y_1=-14 \\ x_2=12 \\ y_2=-12 \end{gathered}`

thus, the equation of the line becomes

`\begin{gathered} But, \\ (dy)/(dx)=(dy)/(dt)*(dt)/(dx) \end{gathered}`

Thus,

`\begin{gathered} Given\text{ that} \\ y=t-5, \\ (dy)/(dt)=1 \\ Also, \\ y=-(1)/(4)x-11 \\ (dy)/(dx)=-(1)/(4) \\ thus, \\ -(1)/(4)=1*(dt)/(dx) \\ \Rightarrow(dx)/(dt)=-4 \end{gathered}`

By integration,

`\begin{gathered} (dx)/(dt)=-4 \\ \Rightarrow\int dx=-4\int dt \\ thus, \\ x=-4t+c \end{gathered}`