The y-intercept will be (0, 4/3). If the y-coordinate of point C is 13. Then the x-coordinate will be 4.
The complete question is given below.
AB and BC form a right angle at their point of intersection, B. If the coordinates of A and B are (14, -1) and (2, 1), respectively, the y-intercept of AB is ____ and the equation of BC is y = __ x + __. If the y-coordinate of point C is 13, its x-coordinate is ___.
A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The equation of the line passing through (14, -1) and (2, 1) will be
(y + 1) = [(1 + 1) / (2 - 14)] (x - 14)
y + 1 = -2/12(x - 14)
y + 1 = - 1/6 (x - 14)
Then the y-intercept of the equation will be
y + 1 = -1/6(-14)
y = 7/3 - 1
y = 4/3
The product of the perpendicular lines is a negative one.
Let m be the slope of the perpendicular line.
Then we have
(-1/6) m = -1
m = 6
Then the equation of the line will be
y = 6x + c
The equation is passing through point B (2, 1). Then we have
1 = 6(2) + c
c = -11
Then the equation will be
y = 6x - 11
If the y-coordinate of point C is 13. Then the x-coordinate will be
13 = 6x - 11
6x = 24
x = 4
More about the linear system link is given below.
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