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4 years ago

A line passes through (1, 3) and (4, 7). Which line would be perpendicular to this line?

Mathematics

1 answer:

GenaCL600 [577]4 years ago

6 0

We can use the points given to solve for the slope.

Slope formula: y2-y1/x2-x1

7-3/4-1

4/3

Find the y-intercept.

y = mx + b

3 = 4/3(1) + b

3 = 4/3 + b

5/3 = b

The slope of a perpendicular line is the opposite and reciprocal.

4/3 -> -3/4

Write the new equation.

y = -3/4x + 5/3

Best of Luck!

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X + y + w = b

White raven [17]

Answer:

(a) a=6 and b≠ $\frac{11}{4}$

(b)a≠6

Step-by-step explanation:

writing equation in agumented matrix form

$\begin{bmatrix}1 &1 & 0 &1 &b\\ 2 &3 & 1 &5 &6\\ 0& 0 & 1 &1 &4\\ 0& 2 & 2&a &1\end{bmatrix}$

now $R_{2} =R_{2}-2\times R_{1}$

$\begin{bmatrix}1 &1& 0 &1 &b\\ 0 &1& 1 &3 &6-2b\\ 0& 0 & 1 &1 &4\\ 0& 2 & 2&a &1\end{bmatrix}$

now $R_{4} =R_{4}-2\times R_{2}$

$\begin{bmatrix}1 &1& 0 &1 &b\\ 0 &1& 1 &3 &6-2b\\ 0& 0 & 1 &1 &4\\ 0& 0 & 0 &a-6 &4b-11\end{bmatrix}$

a) now for inconsistent

rank of augamented matrix ≠ rank of matrix

for that a=6 and b≠ $\frac{11}{4}$

b) for consistent w/ a unique solution

rank of augamented matrix = rank of matrix

a≠6

c) consistent w/ infinitely-many sol'ns

rank of augamented matrix = rank of matrix < no. of variable

for that condition

a=6 and b=[tex]\frac{11}{4}

then rank become 3 which is less than variable which is 4.

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