how do you find the slope when given an equation
?
If it is the equation of a straight line, put it in the form
y = m x + b
(slope intercept form)
m is the slope. The line goes up m units when you move right one unit. (if m is negative of course the line goes down one unit when you go right one unit)
If it is not a straight line, the slope of the tangent to a curve at a point is found by differentiating the function. That is calculus.
then how do you find the slope when only given (x,y) (x,y)
that is not an equation but two points.
I will call them (X1, Y1) and (X2,Y2)
then the slope is
(Y2-Y1) / (X2-X1)
that is how far you went up over how far you went right
i guess
By the way, you can find the equation for the line directly from that.
(Y2-Y1) / (X2-X1) = (y - Y1)/(x-X1)
because the slope to any point (x,y) on the line will be the same as that original slope from the two known points.
To find the slope when given an equation, you need to identify the coefficient of the variable that is raised to the power of 1 (i.e., the variable without any exponent).
Here's a step-by-step explanation to find the slope:
1. Recognize the equation: Make sure the equation is in the form "y = mx + b" or "f(x) = mx + b," where "m" represents the slope.
2. Identify the coefficient: Look for the number that multiplies the variable (x) in the equation. This number is the slope (m).
3. Note the sign: The sign of the coefficient indicates the slope's direction. If it is positive, the slope goes upwards from left to right, and if it is negative, the slope descends from left to right.
4. Interpret the slope: The slope represents the rate at which the dependent variable (y) changes with respect to the independent variable (x). For every one unit increase in the independent variable, the dependent variable changes by the slope amount.
Remember, if the equation is not explicitly in "y = mx + b" form, you may need to manipulate it algebraically to isolate the term with the variable and identify the coefficient multiplying it.
With these steps, you should be able to find the slope from a given equation.