Answer:
The y-intercept of AB is <u>(4/3)</u> and the equation of BC is y = <u>(-1/6)</u> x + <u>(4/3)</u>
If the y-coordinate of point C is 13, its x-coordinate is <u>4</u>.
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Step-by-step explanation:
AB and BC form a right angle at their point of intersection, B.
So, AB ⊥ BC
A = (14 , -1) , B = (2,1)
<u>Part A: Find the y-intercept of AB.</u>
The general equation of the line y = mx + c
Where: m is the slope and c is constant represents y-intercept.
m = (y₂ - y₁)/(x₂ - x₁)
m = 
y = (-1/6) x + c
Substitute with the point (2,1) to find c
1 = (-1/6) * 2 + c
c = 1 + 2 *(1/6) = 4/3
y = (-1/6) x + 4/3
So, <u>the y-intercept of AB is 4/3</u>
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<u>Part B: Find the equation of BC.</u>
BC ⊥ AB at point B
if m is the slope of AB, the slope of BC = (-1/m)
m = (-1/6)
So, the slope of BC = (-1/m) = 6
The equation of the line BC ⇒ y = 6x + c
Substitute with the point (2,1) to find c
1 = 6 * 2 + c
c = 1 - 12 = -11
y = 6x - 11
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<u>Part C: Find x-coordinate of C if y-coordinate of point C is 13.</u>
The equation of the BC is y = 6x - 11
Substitute with the y-coordinate of point C = 13
13 = 6x - 11
6x = 13 + 11 = 24
x = 24/6 = 4
