Given find the equation of the secant line passing through and write your answer in the form

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• Math
• Straight lines

Question:

Last updated: 7/18/2022

Given g(x)=x²-5x, find the equation of the secant line passing through (-3, g (-3)) and (4, g (4)). Write your answer in the form y=mx+b.

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The calculator will find the equation of the secant line that intersects the given curve at the given points, with steps shown.

Related calculators: Line Calculator, Slope-Intercept Form Calculator with Two Points

Your Input

Find the equation of the secant line that intersects the curve $$$f{\left(x \right)} = x^{2} + 1$$$ at $$$x_{1} = 1$$$ and $$$x_{2} = 3$$$.

Solution

Find the y-coordinates of the points on the curve that correspond to the given x-coordinates.

$$$y_{1} = f{\left(x_{1} \right)} = f{\left(1 \right)} = 2$$$

$$$y_{2} = f{\left(x_{2} \right)} = f{\left(3 \right)} = 10$$$

Since we have two points, we can use the line calculator to find the equation of the secant line through the two points.

Thus, the equation of the secant line is $$$y = 4 x - 2$$$.

Answer

The equation of the secant line is $$$y = 4 x - 2$$$A.

We will use the two-point form to find the equation of a secant line.

Answer: The equation of a secant line given two points (a, b) and (c, d) is y - b = [(d - b)/(c - a)] (x - a)

Let's understand the equation of a secant line given two points.

Explanation:

Let two points joining a secant line be (a, b) and (c, d).

The equation of a secant line joining two points (a, b) and (c, d) is y - b = [(d - b)/(c - a)] (x - a)

Here, (d - b)/(c - a) is the slope of the secant line joining the points (a, b) and (c, d).

Consider an example to understand better.

Let's find the equation of a line joining two points (1, 3) and (-2, 5).

Slope = (5 - 3)/(-2 - 1) = -2/3

You can find the slope using Cuemath's Slope Calculator.

Equation of line: y - 3 = -2/3 (x - 1) ⇒ y = (-2/3)x + 2/3 + 3 ⇒ y = (-2/3)x + 11/3 

Thus, the equation of a secant line given two points (a, b) and (c, d) is y - b = [(d - b)/(c - a)] (x - a).

A secant line is simply a linear equation and with two given points you can find the equation.

Explanation:

The two points on the secant line are:

#x = 3 and y = 3^2+2(3)= 15#; coordinate ( 3, 15 )

#x = 5 and y = 5^2+2(5)= #; coordinate ( 5, 35 )

slope of secant line =#=(35-15)/(5-3)=10#

Next, solve for the y-intercept:

#y=mx + b#

#15 = (10)(3)+b#

#b=-15#

secant line equation : #y=10x-15#

hope that helped

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Mark R.

Algebra

7 months, 3 weeks ago

We don’t have your requested question, but here is a suggested video that might help.

Related Question

If g(x)=x/1+2x, how do you find g'(a) and use it to find an equation of the tangent line to the curve at the point (1, 1/3).

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Video Transcript

in order to write the equation of the tangent line, you need two things a point and you need the slope. So in order to find the slope of that tangent line, you need the derivative of G. So you need G. Prime of acts because G is a quotient. Were in use quotient rule. So we want the denominator times the derivative of the top minus the top times the derivative of the bottom over the bottom squared. Clean that up. I have one plus two X minus two X. That's going to give me 1/1 plus two X squared. And that's G prime of X. I want the slope when X is one, so I'm going to find G prime of one That gives me 1/1 plus two is 3. So my slope is 1 9th. Now I'm going to write my equation of my tangent line. So my slope is the 9th And I have the .113 Y equals mx plus B. So one third equals M 1/9 times X plus B. So B is one third minus 1/9 Which is 3/9 -1 9th. So B is two nights. So the equation of your tangent line is why equals slope is 1/9 1 9th, X plus two nights

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