Question

And put output table x -1 y200 x 2 y 0.675 equation is y equals

Answer 1

To find the equation of the line that passes through the points \((-1, 200)\) and \( (2, 0.675)\), we can use the formula for the slope \(m\) of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points:
- \((x_1, y_1) = (-1, 200)\)
- \((x_2, y_2) = (2, 0.675)\)

We can calculate the slope:

\[
m = \frac{0.675 - 200}{2 - (-1)} = \frac{0.675 - 200}{2 + 1} = \frac{-199.325}{3} \approx -66.44167
\]

Next, we use the point-slope form of a line equation, which is:

\[
y - y_1 = m(x - x_1)
\]

We can use point \((-1, 200)\) and the slope \(m\):

\[
y - 200 = -66.44167(x + 1)
\]

To put this in slope-intercept form \(y = mx + b\), distribute and simplify:

\[
y - 200 = -66.44167x - 66.44167
\]

Now, add 200 to both sides:

\[
y = -66.44167x + 200 - 66.44167
\]

\[
y \approx -66.44167x + 133.55833
\]

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

\[
y \approx -66.44x + 133.56
\]

Note: If you need it in a more exact or different form, please specify!