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4 years ago

What is the equation of the line in slope-intercept form? 12 points plz help!!!

Mathematics

1 answer:

Art [367]4 years ago

6 0

Answer: $y=-2x-4$

Step-by-step explanation:

The slope-intercept form of the line is:

$y=mx+b$

Where m is the slope and b the intersection with the y-axis.

You can see in the graph that line intersect the y-axis at $y=-4$ , then:

$b=-4$

Choose two points and substitute them into the formula for calculate the slope. This is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let's pick the points (-4,4) and (-6,8). The the slope is:

$m=\frac{4-8}{-4-(-6)}=\frac{-4}{2}=-2$

Substituting into the equation, you get:

$y=-2x-4$

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[10] In the following given system, determine a matrix A and vector b so that the system can be represented as a matrix equation

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$y=-\frac{158}{579}$

Step-by-step explanation:

To find the matrix A, took all the numeric coefficient of the variables, the first column is for x, the second column for y, the third column for z and the last column for w:

$A=\left[\begin{array}{cccc}1&1&2&2\\-7&-3&5&-8\\4&1&1&1\\3&7&-1&1\end{array}\right]$

And the vector B is formed with the solution of each equation of the system: $b=\left[\begin{array}{c}3\\-3\\6\\1\end{array}\right]$

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$A_{2}=\left[\begin{array}{cccc}1&3&2&2\\-7&-3&5&-8\\4&6&1&1\\3&1&-1&1\end{array}\right]$

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$y=\frac{det(A_{2}) }{det(A)}$

Find the value of the determinant of each matrix, and divide:

$y==\frac{\left|\begin{array}{cccc}1&3&2&2\\-7&-3&5&-8\\4&6&1&1\\3&1&-1&1\end{array}\right|}{\left|\begin{array}{cccc}1&1&2&2\\-7&-3&5&-8\\4&1&1&1\\3&7&-1&1\end{array}\right|} =\frac{158}{-579}$

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