Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
We have the points of a linear function and need to find the equation that represent.
Because it is a linear function, we can find its equation with two points.
We get the points (1,3) and (2,1):
[tex]\begin{gathered} We\text{ call input as x and output as y:} \\ P_1=(x_1,y_1)=(1,3),P_2=(x_2,y_2)=(2,1) \\ y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1) \\ y-3=\frac{(1-3)}{(2-1)}(x-1) \\ y-3=-\frac{2}{1}(x-1)=-2(x-1) \\ y=-2x-2\cdot(-1)+3 \\ y=-2x+2+3 \\ y=-2x+5 \end{gathered}[/tex]We can check that the points (3,-1) and (4,-3) also satisfy the equation that we found above:
[tex]\begin{gathered} \text{For point (3,-1):} \\ y=-2\cdot3+5=-6+5=-1 \\ \text{For point (4,-3):} \\ y=-2\cdot4+5=-8+5=-3 \end{gathered}[/tex]The above shows that the points satisfy the equation.
So, for input=n the output is:
[tex]\text{output}=-2\cdot n+5[/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
