Question

(-2,3)/(2,-1) find the equation

Answer 1

The equation for the line through (-2,3) and (2,-1) is: \(y = -x + 1\).

To find the equation of a line passing through two points
`\((-2,3)\) and \((2,-1)\)`, you can use the point-slope form of a linear equation:
`\(y - y_1 = m(x - x_1)\)`, where
`\((x_1, y_1)\)`is one point on the line, and
`\(m\)` is the slope of the line.

First, determine the slope using the given points. The slope formula between two points
`\((x_1, y_1)\)` and
`\((x_2, y_2)\)` is
`\(m = (y_2 - y_1)/(x_2 - x_1)\)`:

`\[m = (-1 - 3)/(2 - (-2)) = (-4)/(4) = -1\]`

Now that you have the slope
`(\(m = -1\))`and one point
`\((-2,3)\)`, substitute these values into the point-slope form:

`\[y - 3 = -1 \cdot (x - (-2))\]`

Simplify this equation:

`\[y - 3 = -1 \cdot (x + 2)\]`

`\[y - 3 = -x - 2\]`

`\[y = -x - 2 + 3\]`

`\[y = -x + 1\]`

Hence, the equation of the line passing through the points
`\((-2,3)\)` and
`\((2,-1)\)` is
`\(y = -x + 1\)`. This equation represents a line with a slope of -1 and a y-intercept of 1, passing through both given points.