Respuesta :
Answer:
y intercept is 1 1/3
equation is y = -1/6x + 4/3
x coordinate is -70 (-70,13)
Step-by-step explanation:
find M
m = 1 - (-1)/ 2 -1 4
m = -2/12 = -1/6
Find y intercept--Plug m and one point from above into y = mx + b
1 = - 1/6 (2) + b
1 = -2/6 + b
1 2/6 = b
1 1/3 = b
4/3 = b
To find the x coordinate if y is 13
13 = -1/6 x + 4/3
11 2/3 = -1/6 x
-70 = x
Answer:
The y intercept of line AB = [tex](0,\dfrac{4}{3})[/tex]
The equation of line AB will be
[tex] y=\dfrac{-1}{6}x+\dfrac{4}{3}[/tex]
The x-coordinate of C = 4
Step-by-step explanation:
The slope of line AB with coordinates of A and B are (14, -1) and (2, 1)
[tex]m_1=\dfrac{1-(-1)}{2-14}=\dfrac{2}{-12}=\dfrac{1}{-6}[/tex]
The equation of line AB will be
[tex](y-1)=\dfrac{1}{-6}(x-2)\\\\\Rightarrow y=\dfrac{1}{-6}(x-2)+1\\\\\Rightarrow\ y=\dfrac{-1}{6}x+\dfrac{1}{3}+1\\\\\Rightarrow y=\dfrac{-1}{6}x+\dfrac{4}{3}[/tex]
Put x=0, we get the [tex]y=\dfrac{4}{3}[/tex] i.e. [tex](0,\dfrac{4}{3})[/tex] is the y intercept of line AB.
Since, Line AB and Line BC form a right angle at their point of intersection, B. The the product of their slope must be -1.
Therefore, the slope of BC =[tex]m_2=\dfrac{-1}{m_1}=6[/tex]
Let x coordinate of C be a,then the coordinates of C = (a,13)
Now, slope of BC with points B(2,1) and C(a,13) will be
[tex]\dfrac{13-1}{a-2}=6\\\\\Rightarrow\ a-2=\dfrac{12}{6}\\\\\Rightarrow\ a-1=2\\\\\Rightarrow\ a=4[/tex]
Hence, the x-coordinate of C = 4
