Slope graph calculator

Download Article Download Article Finding the Equation of a Tangent Line|Solving Related Problems|Video|Expert Q&A|Tips Unlike a straight line, a curve's slope constantly changes as you move along the graph. Calculus introduces students to the idea that each point on this graph could be described with a slope, or an "instantaneous rate of change." The tangent line is a straight line with that slope, passing through that exact point on the graph. To find the equation for the tangent, you'll need to know how to take the derivative of the original equation. A graph makes it easier to follow the problem and check whether the answer makes sense. Sketch the function on a piece of graph paper, using a graphing calculator as a reference if necessary. Sketch the tangent line going through the given point. (Remember, the tangent line runs through that point and has the same slope as the graph at that point.)Example 1: Sketch the graph of the parabola . Draw the tangent going through point (-6, -1).You don't know the tangent's equation yet, but you can already tell that its slope is negative, and that its y-intercept is negative (well below the parabola vertex with y value -5.5). If your final answer doesn't match these details, you'll know to check your work for mistakes.[1] For function f(x), the first derivative f'(x) represents the equation for the slope of the tangent line at any point on f(x). There are many ways to take derivatives. Here's a simple example using the power rule:[2]Advertisement[3] Read the problem to discover the coordinates of the point for which you're finding the tangent line. Enter the x-coordinate of this point into f'(x). The output is the slope of the tangent line at this point.Example 1 (cont.): The point mentioned in the problem is (-6, -1). Use the x-coordinate -6 as the input for f'(x):f'(-6) = -6 + 3 = -3The slope of the tangent line is -3. The point-slope form of a linear equation is , where m is the slope and is a point on the line.[4] You now have all the information

You need to write the tangent line's equation in this form. If you have a graphing calculator, graph the original function and the tangent line to check that you have the correct answer. If working on paper, refer to your earlier graph to make sure there are no glaring mistakes in your answer.Example 1 (cont.): The initial sketch showed that the slope of the tangent line was negative, and the y-intercept was well below -5.5. The tangent line equation we found is y = -3x - 19 in slope-intercept form, meaning -3 is the slope and -19 is the y-intercept. Both of these attributes match the initial predictions. Here's a run-through of the whole process again. This time, the goal is to find the line tangent to at x = 2:AdvertisementFind the extreme points on a graph. These are points where the graph reaches a local maximum (a point higher than the points on either side), or local minimum (lower than the points on either side). The tangent line always has a slope of 0 at these points (a horizontal line), but a zero slope alone does not guarantee an extreme point. Here's how to find them:[5]Take the first derivative of the function to get f'(x), the equation for the tangent's slope.Solve for f'(x) = 0 to find possible extreme points.Take the second derivative to get f''(x), the equation that tells you how quickly the tangent's slope is changing.For each possible extreme point, plug the x-coordinate a into f''(x). If f''(a) is positive, there is a local minimum at a. If f''(a) is negative, there is a local maximum. If f''(a) is 0, there is an inflection point, not an extreme point.If there is a maximum or minimum at a, find f(a) to get the y-coordinate. The "normal" to a curve at a particular point passes through that point, but has a slope perpendicular to a tangent. To find the equation for the normal, take advantage of the fact that (slope of tangent)(slope of normal) = -1, when they both pass through the same point on the graph.[6] In other

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Point slope form calculatorPoint slope form calculator is an online tool to find the general equation of a line as (y - y1 = m(x - x1). The Point slope calculator is an intuitive tool that lets you calculate the slope and straight-line equation in no time.What is the point-slope form?The point-slope form is defined as the difference in the y-coordinate between two points (y - y1) on a line that is proportional to the difference in the x-coordinate points (x - x1). The point-slope form is about having a single point and a direction and converting that between an algebraic equation and a graph.It can also be stated as: “The equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line.” Point slope formulaThe point slope formula can be expressed as:y - y1 = m(x- x1)Where:m refers to the slope of the linex represents the coordinate on the x-axisy represents the coordinate on the y-axis. The point-slope form is about having a single point and a direction and converting that between an algebraic equation and a graph. We can derive the slope of a line formula from the above point slope form equation.m = (y - y1) / (x- x1)How to find point slope form?The point-slope form can be calculated using the above point slope formula calculator. On the other hand, it can also be calculated using the formula for the point slope form stated above. To find the point slope form manually, follow the steps below:Write down the coordinates for x1, y1, and slopeWrite down the point-slope formula.Substitute the values in the formula and calculate the equation of a line.Point Slope Form Examples:Example 1:Find the equation of the line that passes through (-3, 1) with a slope of 2.Solution:Step 1: Write down the coordinates for x1, y1, and slope m.x1 = -3,y1 = 1, andslope m = 2Step 2: Write down the point-slope formula and apply that formula.y - y1 = m(x- x1)Step 3: Substitute the values in the formula and calculate the equation of a line.y - 1 =2(x - (-3))y - 1 = 2(x + 3)y - 1 = 2x + 6Therefore the Equation = 2x + 6 – y + 1Equation of the line = 2x – y + 7Example 2How do you find the point slope form of points (2, 5) and slope -3?SolutionStep 1: Write down the coordinates for x1, y1, and slope m.x1 = 2,y1 = 5, andslope m = -3Step 2: Write down the point-slope formula and apply that formula.y - y1 = m(x- x1)Step 3:

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