Use the information given to enter an equation in standard form.

Mathematics

1 answer:

Greeley [361]3 years ago

3 0

Answer:

y = -2x + 25

Step-by-step explanation:

A standard equation can be in slope-intercept form: y = mx + b

m is the slope, b is the y-intercept.

Plug in the given slope.

y = -2x + b

To find b, plug in the given point (9, 7).

7 = -2(9) + b

Multiply.

7 = -18 + b

Add 18 to both sides to find b.

25 = b

Plug this into your standard equation.

y = -2x + 25

Check by plugging in the given point again.

7 = -2(9) + 25

7 = -18 + 25

7 = 7

Your answer is correct!

Hope this helps!

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T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)

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

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