Exercises: Linear functions and line equations
Determining the equation of a function.
A line passes through the points and . Determine the equation of the function , the points of intersection and draw the graph for the following values:
For this task you need the following basic knowledge: Linear function
Determining of the function equation
Substitute and into the general line equation .
Use the addition method.
Plug into .
Setze t und m in die allgemeine Geradengleichung ein.
Determining the axis intersection points
Set to determine the intersection with the -axis.
The intersection with the -axis is .
The point of intersection with the -axis corresponds to the -axis intercept
Drawing the graph
Connect either the two intersection points and or the two given points and .
Or choose one of these points and go one to the right and one up according to the slope and connect these two points.
For this task you need the following basic knowledge: Linear function
Determining of the function equation
Substitute and into the general line equation .
Use the addition method.
↓ Plug into .
↓ Plug and into the general line equation.
Determining the axis intersection points
Set to determine the intersection with the -axis.
The intersection with the -axis is .
The point of intersection with the -axis corresponds to the -axis intercept
Drawing the graph
Connect either the two intersection points and or the two given points and .
Or choose one of these points and go one to the right and one up according to the slope and connect these two points.
For this task you need the following basic knowledge: Linear function
Determining of the function equation
Substitute and into the general line equation .
Use the addition method.
Shorten the fractions.
Plug into .
Multiply.
Subtract.
Setze m und t in die allgemeine Geradengleichung ein.
Determining the axis intersection points
Set to determine the intersection with the -axis.
Divide the fractions
The intersection with the -axis is
The point of intersection with the -axis corresponds to the -axis intercept
Drawing the graph
Connect either the two intersection points and or the two given points and .
Or choose one of these points and go 3 to the right and 2 down according to the slope and connect these two points.
For this task you need the following basic knowledge: Linear function
Determining of the function equation
Substitute and into the general line equation .
Use the addition method.
Plug into .
Subtract.
Plug and into the general line equation.
Determining the axis intersection points
Set to determine the intersection with the -axis.
Divide the fractions. Multiply by the inverse.
Multiply.
The intersection with the -axis is .
The point of intersection with the -axis corresponds to the -axis intercept
Drawing the graph
Connect either the two intersection points and or the two given points and .
Or choose one of these points and go 7 to the right and 2 up according to the slope and connect these two points.
For this task you need the following basic knowledge: Linear function
Determining of the function equation
Substitute and into the general line equation .
Use the addition method.
Plug into .
Multiply.
Plug and into the general equation of a straight line.
Determining the axis intersection points
Set to determine the intersection with the -axis.
Divide the fractions. That means, multiply by the inverse.
Multiply.
The intersection with the -axis is
The point of intersection with the -axis corresponds to the -axis intercept
Drawing the graph
Connect either the two intersection points and or the two given points and .
Or choose one of these points and go 14 to the right and 11 down according to the slope and connect these two points.
For this task you need the following basic knowledge: Linear function
Determining of the function equation
Substitute and into the general line equation .
Use the addition method.
Divide.
Plug into .
Multiply.
Plug and into the general equation of a straight line.
Determining the axis intersection points
Set to determine the intersection with the -axis.
The intersection with the -axis is
The point of intersection with the -axis corresponds to the -axis intercept
Drawing the graph
Connect either the two intersection points and or the two given points and .
Or choose one of these points and go 1 to the right and 0.8 up according to the slope and connect these two points.