Correct the error:

Question

Question: Find the point-slope equation of the line with slope -3 that passes through the point (2,-10).
Solution:

What is the error? Explain how to solve the problem.

Answer 1

The error is that the solution does not provide the correct point-slope equation of the line.

To solve the problem, we can use the point-slope form of a linear equation. The point-slope form is given by y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line.

In this case, the slope is given as -3 and the point (2, -10) is on the line. Substituting these values into the point-slope form, we get:

y - (-10) = -3(x - 2)

Simplifying this equation, we get:

y + 10 = -3x + 6

Subtracting 10 from both sides, we have:

y = -3x - 4

So, the correct point-slope equation of the line with slope -3 that passes through the point (2, -10) is y = -3x - 4.