Question

Through: (-1,-2), slope:
3
2

Answer 1

The equation of the line with a slope of
`\( (3)/(2) \)` passing through the point
`\((-1, -2)\)` is
`\( y = (3)/(2)x - (1)/(2) \)`.

To find the equation of a line given a point and the slope, you can use the point-slope form of the equation:

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

where \((x_1, y_1)\) is a point on the line, and m is the slope.

Given the point
`\((-1, -2)\)` and the slope
`\(m = (3)/(2)\)`, substitute these values into the point-slope form:

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

Simplify the equation:

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

Distribute the
`\((3)/(2)\)`:

`\[y + 2 = (3)/(2)x + (3)/(2)\]`

Subtract 2 from both sides to isolate y:

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

Combine the constants:

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

So, the equation of the line with a slope of
`\( (3)/(2) \)` passing through the point
`\((-1, -2)\)` is
`\( y = (3)/(2)x - (1)/(2) \)`.

The probable question may be: "Find the equation of a line given a point and the slope where point is (-1,-2) and slope is 3/2"