Question

Express it in slope
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000
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-8
8
In slope-intercept form

Answer 1

In this question, we are given two points, (0,0) and (-8,8), and we want to find the equation of the line in slope-intercept formula.

Slope-intercept formula:

The equation of a line, in slope-intercept formula, is given by:

$y = mx + b$

In which m is the slope and b is the y-intercept(value of y when x = 0)[/tex]

Point (0,0):

This means that when $x = 0, y = 0$, and thus, the y-intercept is $b = 0$, and the equation of the line is:

$y = mx$

Slope:

When we have two points, the slope is given by the change in y divided by the change in x.

In this question, the two points are (0,0) and (-8,8).

Change in x: -8 - 0 = -8

Change in y: 8 - 0 = 8

Slope:

$m = \frac{-8}{8} = -1$

Thus, the equation of the line, in slope-intercept formula, is:

$y = -x$

For another example of an equation of a line in slope-intercept formula, you can check https://brainly.com/question/21010520

Answer 2

The equation of the line that passes through $(x_{1}, y_{1}) = (0, 0)$ and $(x_{2}, y_{2}) = (-8, 8)$ is $y = -x$.

According to the statement, we know the location of two Points: $(x_{1}, y_{1}) = (0, 0)$ and $(x_{2}, y_{2}) = (-8, 8)$, and must derive the Equation of the Line from this information, whose procedure is described below:

1) Determine the Slope of the line by the Slope Equation for Secant Lines.

2) Use ($x_{1}, y_{1}$) in the Equation of the Line and solve for the Intercept.

3) Write the resulting Equation of the Line.

Step 1:

The slope of a secant line ($m$) is calculated from the following formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ (1)

If we know that $(x_{1}, y_{1}) = (0, 0)$ and $(x_{2}, y_{2}) = (-8, 8)$, then the slope of the line is:

$m = \frac{8-0}{-8-0}$

$m = -1$

Step 2:

The equation of the line is Slope-Intercept Form is now represented:

$y = m\cdot x + b$ (2)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$b$ - Intercept.

If we know that $(x_{1}, y_{1}) = (0, 0)$ and $m = -1$, then the intercept of the equation of the line is:

$0 = -1\cdot (0) + b$

$b = 0$

Step 3:

And the equation of the line that passes through $(x_{1}, y_{1}) = (0, 0)$ and $(x_{2}, y_{2}) = (-8, 8)$ is $y = -x$.

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