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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)
