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What is the equation of the line that passes through the point (-2, 10) and has a slope of -4?

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Final answer:

The equation of the line that passes through the point (-2, 10) with a slope of -4 is y = -4x + 2.

Step-by-step explanation:

The equation of a line that passes through a specific point and has a given slope can be found using the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes and m is the slope of the line. For a line that passes through the point (-2, 10) with a slope of -4, the equation can be written as:

y - 10 = -4(x - (-2)).

Simplifying this, we get:

y - 10 = -4x - 8

Adding 10 to both sides to get y by itself, we find the equation in slope-intercept form:

y = -4x + 2.

This is the linear equation of the line with the given characteristics.

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