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2x - 3y = - 13
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
First obtain the equation in slope-intercept form
y = mx + c ( m is the slope and c the y-intercept )
calculate m using the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, 5 ) and (x₂, y₂ ) = (- 2, 3 )
m = =
=
y = x + c ← partial equation
to find c substitute either of the 2 points into the partial equation
using (1, 5 ), then
5 = + c ⇒ c =
rearrange the equation into standard form
multiply through by 3
3y = 2x + 13 ( subtract 3y and 13 from both sides )
2x - 3y = - 13 ← in standard form
Answer:
The number of ways are there to paint the four buildings is 48.
Step-by-step explanation:
I) let the first building be any color. Therefore the first building can be painted with any of the 4 colors.
Therefore the first building can be colored in 4 ways.
ii) the second building can be colored in 3 ways since it cannot be colored the
same color as the first building.
iii) the third building can also be colored in 3 ways.
iv) the last building can be colored in 2 ways because it cannot be the same color as the first building or the color of the adjacent building.
Therefore the total number of ways the buildings can be colored = 4 3
3
2 = 48.