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A line passes through the point [tex](-2,-2)[/tex] and has a slope of [tex]-3[/tex]. Write an equation in point-slope form for this line.

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Sagot :

GinnyAnswer
To find the equation of a line given a point it passes through and its slope, we use the point-slope form of a linear equation. The point-slope form is given by

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

where [tex]\((x_1, y_1)\)[/tex] is a point on the line, and [tex]\(m\)[/tex] is the slope of the line.

Given:
- The point [tex]\((-2, -2)\)[/tex]
- The slope [tex]\(m = -3\)[/tex]

Substitute the given point and slope into the point-slope form:

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

Simplify the equation by handling the double negatives:

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

This equation,

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

is in the point-slope form and represents the line that passes through the point [tex]\((-2, -2)\)[/tex] with a slope of [tex]\(-3\)[/tex].
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