What is the equation of a line with a slope of -3 that passes through the point (2, 4)?

To determine the correct equation of a line with a slope of -3 that passes through the point (2, 4), we start by using the point-slope form of a linear equation, which is represented as:

y - y1 = m(x - x1)

In this equation, m is the slope, and (x1, y1) is a point on the line. Here, we know the slope m is -3 and the point is (2, 4). Substituting these values into the equation gives us:

y - 4 = -3(x - 2)

Next, we will simplify this equation to slope-intercept form, which is y = mx + b. Distributing the -3, we have:

y - 4 = -3x + 6

To isolate y, we add 4 to both sides:

y = -3x + 6 + 4

This simplifies to:

y = -3x + 10

So the equation of the line is y = -3x + 10. This confirms that the correct answer is indeed the equation that states the line has a slope of -3 and passes through the point (2, 4).

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