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The gradient of a linear equation is also known as slope. Slope is the (Change in Y)/(Change in X). Luckily there is a simple way to find out the slope in a simple linear equation. A simple linear equation can be written as: y = mx + b where m = slope (gradient) and b = y-intercept I assume your equation is x = 2y + 1. This may look like it fits the equation above but it does not. The equation needs to be solved for y. x = 2y + 1 (Subtract 1 from both sides) x - 1 = 2y (Divide both sides by 2) x/2 - 1/2 = y Now the equation is in the proper form. y = 1/2x - 1/2 Looking at the first equation: m = slope = 1/2. The slope (or gradient) is 1/2
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What is gradient y equals x2 when -2?
4
What is the inverse of a function y1?
Definition of the inverse of a function.Let f and g be two functions such thatf(g(x)) = x for every x in the domain of g andg(f(x)) = x for every x in the domain of f.The function g is the inverse of the function f, and the domain of f is equal to the range of g, and vice versa.Example: Find the inverse of y1 = 2x + 7Solutiony1 = 2x + 7 interchange x and y;x = 2y1 + 7 solve for y;x - 7 = 2y1 + 7 -7 subtract 7 to both sides;x - 7 = 2y1 divide by 2 both sides;(x - 7)/2 = y1 replace y1 with y2;y2 = (x - 7)/2Thus, the inverse of y1 = 2x +7 is y2 = (x -7)/2Let's check if this is true according to the above definition:Let y1 = f(x) = 2x +7 and y2 = g(x) = (x -7)/21. f(g(x))= x ?f(x) = 2x + 7f((x - 7)/2) = 2[(x -7)/2] + 7 = x - 7 + 7 = x True2. g(f(x) = x ?g(x) = (x - 7)/2g(2x + 7) = [(2x + 7) - 7]/2 = 2x/2 = x True
How do you find the gradient of the curve y equals x-4 over x when y equals 3?
y = x - 4/x so gradient = dy/dx = 1 + 4/x2 When y = 3, x - 4/x = 3 x2 - 3x - 4 = 0 so x = -1 or x = 4 When x = -1, gradient = 1 + 4/(-1)2 = 1 + 4/1 = 1+4 = 5 When x = 4, gradient = 1 + 4/(4)2 = 1 + 4/16 = 1+1/4 = 1.25
Can a gradient of a line be 0?
Theoretically, yes. For lines parallel to y-axis, gradient is zero. Eg, x=4.
The gradient of the line is y equals -4 x plus 3 is?
When equation of line is y=-4x+3, Gradient is -4 (as seen from the coefficient of x) and the y-intercept is +3 (point where x=0)
The gradient of x y2?
x+y=2 the gradient is -1
What is the gradient of the tangent to the curve at x equals 2 if Y equals x2?
Gradient to the curve at any point is the derivative of y = x2 So the gradient is d/dx of x2 = 2x. When x = 2, 2x = 4 so the gradient of the tangent at x = 2 is 4.
What is gradient y equals x2 when -2?
4
What is the inverse of a function y1?
Definition of the inverse of a function.Let f and g be two functions such thatf(g(x)) = x for every x in the domain of g andg(f(x)) = x for every x in the domain of f.The function g is the inverse of the function f, and the domain of f is equal to the range of g, and vice versa.Example: Find the inverse of y1 = 2x + 7Solutiony1 = 2x + 7 interchange x and y;x = 2y1 + 7 solve for y;x - 7 = 2y1 + 7 -7 subtract 7 to both sides;x - 7 = 2y1 divide by 2 both sides;(x - 7)/2 = y1 replace y1 with y2;y2 = (x - 7)/2Thus, the inverse of y1 = 2x +7 is y2 = (x -7)/2Let's check if this is true according to the above definition:Let y1 = f(x) = 2x +7 and y2 = g(x) = (x -7)/21. f(g(x))= x ?f(x) = 2x + 7f((x - 7)/2) = 2[(x -7)/2] + 7 = x - 7 + 7 = x True2. g(f(x) = x ?g(x) = (x - 7)/2g(2x + 7) = [(2x + 7) - 7]/2 = 2x/2 = x True
How do you calculate a gradient of a graph?
Y divided by X axix- Y/X
How can you tell whether the gradient of a curve is increasing or decreasing?
Differentiate the curve twice and then enter a value for x. If the answer is positive, the gradient is increasing at that point. If the answer is negative, the gradient is decreasing at that point. And if the answer is zero, the gradient is not changing.
How do you find the gradient of the curve y equals x-4 over x when y equals 3?
y = x - 4/x so gradient = dy/dx = 1 + 4/x2 When y = 3, x - 4/x = 3 x2 - 3x - 4 = 0 so x = -1 or x = 4 When x = -1, gradient = 1 + 4/(-1)2 = 1 + 4/1 = 1+4 = 5 When x = 4, gradient = 1 + 4/(4)2 = 1 + 4/16 = 1+1/4 = 1.25
Can a gradient of a line be 0?
Theoretically, yes. For lines parallel to y-axis, gradient is zero. Eg, x=4.
The gradient of the line is y equals -4 x plus 3 is?
When equation of line is y=-4x+3, Gradient is -4 (as seen from the coefficient of x) and the y-intercept is +3 (point where x=0)
What is a positive gradient in math?
A positive gradient is a characteristic of a function whose value increases as the value of the argument increases. So, if y is a function, f(x), of x, then an increase in the value of x is accompanied by an increase in the value of y.
What is the gradient of y 3x 5?
The gradient of the function y = 3x + 5 is simply the coefficient of x, which is 3. In this context, the gradient represents the slope of the line that the function represents. This means that for every unit increase in x, y will increase by 3 units.
What is gradient of a line?
The slope. The gradient of a straight line is the number of co-ordinates on the y axis to one co-ordinate on the x axis.
