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

User FireSnake
by
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1 Answer

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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"

User TMtech
by
7.6k points

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