Identify the equation in slope-intercept form for the line containing the point (-4,1) and (2,3)

Mathematics

1 answer:

oksano4ka [1.4K]3 years ago

7 0

Answer:

The point slope formula is

(y−y1)=m(x−x1)

Where m = the slope calculated as y2−y1x2−x1

(x1,y1)(x2,y2)

(-4 , 1) (-2 , 3)

Solve for the slope

m = 3−1−2−(−3) = 21 = m = 2

(y−3)=2(x−(−2)) Plug in known values.

y−3=2(x+2) Simplify signs

y−3=2x+4 Use Distributive property

y=−2x+4+3 isolate the y variable

answer (y = −5x+7 ) Simplify

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A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.

Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)

and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)

So, the matrix of the transformation is

$\left[\begin{array}{ccc}7&6\\4&5\end{array}\right]$

The inverse of the matrix is

$\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]$

So, the Inverse Transformation is given by

$T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})$