(0,1) and (-2,-2)

Answer 1

It looks like you've provided two points: (0,1) and (-2,-2). Do you need help finding the equation of the line that passes through these points?

If so, here’s how you can do it:

First, calculate the slope (m) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Here, \((x_1, y_1) = (0, 1)\) and \((x_2, y_2) = (-2, -2)\). Substituting in the values gives:
\[ m = \frac{-2 - 1}{-2 - 0} \]
\[ m = \frac{-3}{-2} \]
\[ m = \frac{3}{2} \]

Now that we have the slope \(m = \frac{3}{2}\), we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]

Using the point (0,1):
\[ y - 1 = \frac{3}{2}(x - 0) \]

Simplify this equation to get it into slope-intercept form (y = mx + b):
\[ y - 1 = \frac{3}{2}x \]
\[ y = \frac{3}{2}x + 1 \]

So the equation of the line that passes through the points (0,1) and (-2,-2) is:
\[ y = \frac{3}{2}x + 1 \]

If you need any more details or further explanations, feel free to ask!