What is the equation in point-slope form of the line that passes through the point (3, −2) and has a slope of 23?

Question

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Response areaResponse areaResponse area=Response area(Response areaResponse areaResponse area)

Answer 1

The point-slope form of the equation of a line is given by the formula:

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

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

Given the point \( (3, -2) \) and the slope \( m = 23 \):

1. \( x_1 = 3 \)
2. \( y_1 = -2 \)
3. \( m = 23 \)

Plugging these values into the point-slope formula, we get:

\[ y - (-2) = 23(x - 3) \]

This simplifies to:

\[ y + 2 = 23(x - 3) \]

Now, mapping the equation into the specified parts:

1. Response area: \( y + 2 \)
2. Response area: \( 23 \)
3. Response area: \( x - 3 \)

The complete equation in point-slope form is:

\[ y + 2 = 23(x - 3) \]