Given:
The equation of a line is:

The line is dilated by factor 3.
To find:
The result of dilation.
Solution:
The equation of a line is:

For
,




For
,




Divide both sides by 2.


The given line passes through the two points A(0,5) and B(2,2).
If the line dilated by factor 3 with origin as center of dilation, then

Using this rule, we get


Similarly,


The dilated line passes through the points A'(0,15) and B'(6,6). So, the equation of dilated line is:




Multiply both sides by 2.



Therefore, the equation of the line after the dilation is
.
X^2 - 5x + 4
-2x^2 + 10x -8
We are asked to find the equivalent of the expression given:
(3m⁻² n)⁻³
-----------
6mn⁻²
Perform distribution of power using power rule such as shown below:
3⁻³ m⁻²*⁻³n⁻³
-----------------
6mn⁻²
Perform product and quotient rule such as shown below:
m⁶ n²
--------
3³ *6*m*n³
Simplify,
m⁵
--------
162n
The answer is m⁵/162n.
The slope of this graph is 6