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What linear function includes the points -2 4 0 5 and 2 6 and how do you get the answer?
Zxcasdqwe3
The three points are collinear since a straight line is passing through them. If you compute the slope in terms of two points, you will find the same slope, which is 1/2.
Let's see this:
(-2, 4) and (0.5)
m = (5 - 4)/(0 - (-2))= 1/2
(-2, 4) and (2, 6)
m = (6 - 4)/(2 - (-2)) = 2/4 = 1/2
((0, 5) and (2, 6)
m = (6 - 5)/(2 - 0) = 1/2
To find the equation of the line that passes through these three points, you need to use only one of them. Let's use the point (0, 5).
(y - y1) = m(x - x1)
(y - 5) = (1/2)(x - 0)
y - 5 = (1/2)x
y -(1/2)x - 5 = 0 This is the equation that you are looking for.
You will find the same equation if you use two other points.
Check.
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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?
To be generated by a linear function the points must all lie on a straight line of the form y = mx + cTo 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 + 6Now 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)Therefore all the points lie of the same line and are all generated by a linear function.
When is a linear function considered to be a direct variation?
Direct variation means that a linear function can be written as y = kx. The y-intercept must be (0, 0). The constant, k, is the slope.
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.
When the slope is 0 and the y-intercept is 4 is the function linear?
The line will be parallel to the x axis cutting through the y axis at (0, 4)
What is the difference of x-intercept and y-intercept?
The x- and y-intercepts of a function are the points at which the graph of the function crosses respectively the x- and y-axis (ie. y=0 and x=0).
Is a linear function a direct variation?
yes * * * * * No, it is not. In a direct variation, if one of the variables is 0, the other MUST also be 0. In a linear function, they will be the intercepts.
Is 3y plus 2 equals 0 a linear function?
It is not a linear function because it is missing x as the input variable
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?
To be generated by a linear function the points must all lie on a straight line of the form y = mx + cTo 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 + 6Now 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)Therefore all the points lie of the same line and are all generated by a linear function.
When is a linear function considered to be a direct variation?
Direct variation means that a linear function can be written as y = kx. The y-intercept must be (0, 0). The constant, k, is the slope.
What linear function gives you f(0) 1 and f(1) 4?
Consider it as a graph with points (x, f(x)): you have two points (0, 1) and (1, 4) joined by a line (as it is a linear function). The slope m = change in y/change in x = (4-1)/(1-0) = 3 Using y - Yo = m(y - Xo) y - 1 = 3(x - 0) → y = 3x + 1 → f(x) = 3x + 1
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.
Is there a difference between linear equations and functions?
A linear equation IS a function. A function can look like X2+X+C, or X3+0, or X+Y+C, or many other ways. The function X+Y+C is a function in two variables, and can be a linear equation.
How do you find the average rate of change for a linear function?
A linear function has a constant rate of change - so the average rate of change is the same as the rate of change.Take any two points, A = (p,q) and B = (r, s) which satisfy the function. Then the rate of change is(q - s)/(p - r).If the linear equation is given:in the form y = mx + c then the rate of change is m; orin the form ax + by + c = 0 [the standard form] then the rate is -a/b.
If second derivative is 0 and third derivative is 0 What is true about that point?
If the second derivative of a function is zero, then the function has a constant slope, and that function is linear. Therefore, any point that belongs to that function lies on a line.
Is the direct variation of two variables always a linear function?
YES...A direct variation is a linear relationship in which y-intercept is always 0.
Is y equal xsquare minus 4 a linear function?
No. That function describes a parabola who's vertex is at the point (0, -4).
How do you know a function is linear?
If the variable x is raised to the power of 1 or 0. No other possibilities.
