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You find the slope by using 2 points and doing y2-y1/x2-x1
Then you put it into the equation and plug in any point as x or y and find b. Then, you plug in x and y values and graph them.
What is written above is correct, but does not answer the question. The method provided above is only valid för functions of the form: f(x) = kx + m
However when dealing with polynomials such as x^3, where the slope is under constant change, the slope is calculated using a different method.
lim h-->0 (f(x+h) - f(x))/h
Simplification is needed for, for example the calculation of the slope of x^3 at any given point for x. Try it out yourself. The answer is 3x^2. Generally: if f(x)=x^n then f´(x)=nx^(n-1)
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How does the graph of an exponential function differ from the graph of a linear function and how is the rate of change different?
The graph of a linear function is a line with a constant slope. The graph of an exponential function is a curve with a non-constant slope. The slope of a given curve at a specified point is the derivative evaluated at that point.
What does slope mean in algebra?
Slope in algebra refers to the rate of change of a function at a given point. This can be used in physics, where on a graph that shows the change in velocity, the value of the slope is equal to the acceleration at that moment in time.
How do you get the tangent line without the graph?
The answer will depend on the context. If the curve in question is a differentiable function then the gradient of the tangent is given by the derivative of the function. The gradient of the tangent at a given point can be evaluated by substituting the coordinate of the point and the equation of the tangent, though that point, is then given by the point-slope equation.
What is the linear parent function?
The linear parent function is y=x. The line on a graph passes through the origin(0,0) with a slope of 1. The line will face left to right on the graph like this /.
What does k correspond to in a direct variation function?
k is the constant of variation and is the gradient (slope) of the relevant graph.
