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Would the set of points -3 -3 and -2 0 and -1 3 and 0 6 and 1 9 and 2 12 have been generated by a linear function?
Wiki User
∙ 7y ago
To be generated by a linear function the points must all lie on a straight line of the form y = mx + c
To check if these points do so lie on such a line, use two of the points to find the equation of the line (using the point-gradient form of (y - Y) = m(x - X) where m is the gradient of the lines and (X, Y) is a point on the line) and then substitute in the x values of the other points and check if the calculated y value is correct:
Use the first two points (-3, -3) and (-2, 0) to find the line between those those points on which the other points must lies:
gradient = change_in_y / change_in_x
→ m = (0 - -3).(-2 - -3) = 3/1 = 3
→ y - 0 = 3(x + 2)
→ y = 3x + 6
Now to test the other points:
- (-1, 3): y = 3×-1 + 6 = -3 + 6 = 3 (as required)
- (0, 6): y = 3×0 + 6 = 6 (as required)
- (1, 9): y = 3×1 + 6 = 3 + 6 = 9 (as required)
- (2, 12): y = 3×2 + 6 = 6 + 6 = 12 (as required)
Wiki User
∙ 7y ago
Wiki User
∙ 7y agoObviously! A linear function must represent a linear relation and conversely. That is why they are both called "linear".
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What do you call a function whose graph is a non-vertical line?
It is a function. If the graph contains at least two points on the same vertical line, then it is not a function. This is called the vertical line test.
What distinguishes a linear function from other functions?
A linear function is one in which the power of the function is only one. So, the graph of it would be a straight line. For example, x2 + x = y is not linear, because the highest power is 2. A main difference is, non linear functions have curves, where as a linear function is a straight line, with the exception of when the function has a power of 0, and it is technically a straight line.
Can a linear function not have a y-intercept?
No, it would have to be parallel to the y-axis, making the slope undefined and having only a single x-value. Not a linear function.
How do you find for the zero of a linear function?
If it is a linear function, it is quite easy to solve the equation explicitly, using standard methods of equation-solving. For example, if you have "y" as a function of "x", you would have to solve the variable for "x".
How would you find the equation for a linear function when you are given a table of values for the variables?
If the figures in the table are exact and without measurement error then take any two of the points (x1, y1) and (x2, y2) and use these to form the linear relation y - y1 = ((y2 - y1)/(x2 - x1))(x - x1) If, however, you suspect that the values in the table do not exactly follow a linear relationship then use linear regression for which formulae are provided in wikipedia.
What do you call a function whose graph is a non-vertical line?
It is a function. If the graph contains at least two points on the same vertical line, then it is not a function. This is called the vertical line test.
Is a line with an infinite amount of slope a linear function?
No, I don't think that would fit the definition of a linear function.
How is Linear motion generated?
passing a rope over a puley would be the simplest method of converting rotary movement to linear. (or vice-versa).
Is the sum of two linear functions always a linear function?
Yes. You would have to multiply to change it.
What distinguishes a linear function from other functions?
A linear function is one in which the power of the function is only one. So, the graph of it would be a straight line. For example, x2 + x = y is not linear, because the highest power is 2. A main difference is, non linear functions have curves, where as a linear function is a straight line, with the exception of when the function has a power of 0, and it is technically a straight line.
Can a linear function not have a y-intercept?
No, it would have to be parallel to the y-axis, making the slope undefined and having only a single x-value. Not a linear function.
How do you find for the zero of a linear function?
If it is a linear function, it is quite easy to solve the equation explicitly, using standard methods of equation-solving. For example, if you have "y" as a function of "x", you would have to solve the variable for "x".
How do you know that a table value is a linear function?
There are several ways to do that. For example, you can actually graph the function. Or, you can check the ratio of the differences between the points. If this ratio (change in y, divided by change in x) is constant, the function is linear.
What is a difference between DC and ac resistance and expline DC resistasce?
DC is just direct current into a resistance it is a linear function. AC if the resistance is non reactive it would be the same linear function.
What is the molecule shape of CBr?
Linear. Any 2 atoms bonded are linear because 2 points make a line. It would be impossible to get any other shape.
How would you find the equation for a linear function when you are given a table of values for the variables?
If the figures in the table are exact and without measurement error then take any two of the points (x1, y1) and (x2, y2) and use these to form the linear relation y - y1 = ((y2 - y1)/(x2 - x1))(x - x1) If, however, you suspect that the values in the table do not exactly follow a linear relationship then use linear regression for which formulae are provided in wikipedia.
What is the definition of linear plot?
if two points are plotted and then the third point falls in line with the other two. i.e. (1,1), (2,2), (3,3). these would create a linear plot.
