Question
Sketch an example of a linear function in graph form.
Hint:
The graph of a linear function is always a straight line. So we sketch a straight line in a graph and find its equation in the slope intercept form, which is y = mx + c, where m is the slope of the line and c is the y intercept.
The correct answer is: y=x
We shall draw a straight line through the origin as shown below.
We will now derive the equation of this line in slope intercept form.
The slope intercept form is
y = mx + c
Where m is the slope and c is the y intercept.
From the graph, we can see that the line cuts the y axis at 0
So, c = 0
The slope between two points (a, b) and (c, d) is given by
We take any two points from the graph to be
(a, b) = (1,1) and (c, d) = (2, 2)
Calculating the slope, we have
Putting the value of m and c in the equation, we get
y = 1.x
That is
y = x
This is a linear equation.
This is a linear equation.
We can take any straight line in the xy plane and derive its equation in the above method; we will get a linear function. We can check this by calculating the slope between all the points. If the slope is constant everywhere, then it is linear.
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There are other ways to determine if a given equation is linear or not. If an equation can be written in the form y = ax + b, where a and b are constants, then the function is linear. Another way to check if an equation is linear is by checking the highest degree of a term in the equation. If the highest degree of any term in the equation is 1, then the equation is linear, and if the degree of any term is greater than 1, then the equation is non-linear.
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There are other ways to determine if a given equation is linear or not. If an equation can be written in the form y = ax + b, where a and b are constants, then the function is linear. Another way to check if an equation is linear is by checking the highest degree of a term in the equation. If the highest degree of any term in the equation is 1, then the equation is linear, and if the degree of any term is greater than 1, then the equation is non-linear.
Determine whether the following functions are linear or non-linear and explain how you know.
There are other ways to determine if a given equation is linear or not. If an equation can be written in the form y = ax + b, where a and b are constants, then the function is linear. Also, the graph of a linear equation is always a straight line. So, we can plot a graph of the given equation and check if it is a straight line.
Determine whether the following functions are linear or non-linear and explain how you know.
There are other ways to determine if a given equation is linear or not. If an equation can be written in the form y = ax + b, where a and b are constants, then the function is linear. Also, the graph of a linear equation is always a straight line. So, we can plot a graph of the given equation and check if it is a straight line.
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Explain why it would be beneficial to choose the inputs -8, -4, 0 , 4, and 8 for the function
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Explain why it would be beneficial to choose the inputs -8, -4, 0 , 4, and 8 for the function
Integral values means the value of an integer, that is, the value should be number, either positive or negative. The above method of choosing x in such a way that there is no fraction or square root left is a very important trick required while making a graph of the equation.
Make and test a conjecture about the sum of numbers from 1 to 7. Write a conjecture for the general case.
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Graph the following functions by filling out the X/Y chart using the given inputs
| X | -7 | -6 | -3 | 2 | 9 |
| Y |
We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. Either way, we need points satisfying the equation to plot its graph.
Graph the following functions by filling out the X/Y chart using the given inputs
| X | -7 | -6 | -3 | 2 | 9 |
| Y |
We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. Either way, we need points satisfying the equation to plot its graph.
