Determine the intercepts of the line. Do not round your answers. 2x+5y=-6, y x-intercept:

Mathematics

1 answer:

NikAS [45]1 year ago

3 0

The required x and y-intercept of the given line is -3 and -6/5 respectively.

<h3>What is the slope of the line?</h3>

The slope of the line is the tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The given equation of the line is 2x+5y=-6.
Transform into standard form of line .i.e is y = mx + c

5y = -2x - 6
y = -2x/5 - 6/5
here , m = -2/5 and c = -6/5
Since c = y-intercept of the line = -6/5
Now, put y = 0 in the equation of the line.
2x = -6
x = -3

Thus, the required x and y-intercept of the given line is -3 and -6/5 respectively.

Learn more about slopes here:
brainly.com/question/3605446

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2 years ago

-x=-y+2 and 3y+4=2x solve using matrices

MissTica

$\begin{cases}-x=-y+2\\3y+4=2x\end{cases}\implies\begin{cases}x-y=-2\\2x-3y=4\end{cases}$

In matrix form, this is

$\begin{bmatrix}1&-1\\2&-3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-2\\4\end{bmatrix}$

The coefficient matrix has determinant

$\begin{vmatrix}1&-1\\2&-3\end{vmatrix}=-3+2=-1\neq0$

so it has an inverse, which is

$\begin{bmatrix}1&-1\\2&-3\end{bmatrix}^{-1}=\begin{bmatrix}3&-1\\2&-1\end{bmatrix}$

Multiply both sides by the inverse matrix:

$\begin{bmatrix}3&-1\\2&-1\end{bmatrix}\begin{bmatrix}1&-1\\2&-3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}3&-1\\2&-1\end{bmatrix}\begin{bmatrix}-2\\4\end{bmatrix}$